Glossary

This glossary lists, in alphabetical order, the terms a reader meets in this wiki: the Broken-Born program’s own vocabulary, such as the velocity gate, the wave island, the momentum graviton and the three debts, and the established physics the program draws on, such as Lagrangian polarizations, the Fierz–Pauli mass term and the Kibble mechanism. Each entry says in plain words what the term means and links the page that defines it, where the term’s status and the evidence for it are given. Some words mean different things in different documents or sections; their entries are marked as collisions and gathered in a list near the end, which is followed by the acronyms. Mathematical symbols are on the Notation page and cited works on the References page.

Status: Record. A register compiled from the wiki’s pages; it makes no claims of its own and carries no provenance tags of its own. Each term’s status, tags and verification are on the page it links, and where an entry and that page differ, the page and its sources govern.

Using the glossary#

Entries. Each entry gives the meaning first and then the page that defines it. Program terms and established physics share one alphabet, and the linked page says which a term is. Closely related terms share an entry and are named together at its head.
Order. Greek letters sort by their English names (α under A, χ under C, ψ under P, ρ under R, τ under T), and ’t Hooft sorts under T. Terms that begin with a number or a mark come first, under Numbers and marks.
Status in titles. Page titles show status. “Obituary: …” marks a dead claim, “Open: …” an open problem, with its number OPn when #11 §14 lists it, and “Row n: …” a test in the predictions table; “(superseded)”, “(chat-only)” and “(popsci-only)” mark the remaining cases. Established physics and standing program claims carry no marker. A minor item of another status inside a page has a heading of its own, such as “Open: …” or “Superseded: …”, which the registers under Status link.
Collisions. Words such as gate, soliton, island, frame and dual mean different things in different places. Their entries are marked Collision, and the Collisions section lists them all.
Names kept, metaphors not. The program’s own names keep their wording: “the debts” is the lab notebook’s name for its three most severe open problems. Where #11 writes “two ledgers” or “the conjugate ledger” (§10 and Appendix A), the wiki writes “two descriptions”. HANDOFF.md §7 and the root CLAUDE.md record that ledger and bookkeeping metaphors do not work for Paul, and the wiki quotes such phrases only as history.
Documents. “#1” to “#15” are the artifact numbers of HANDOFF.md §3: #1 the lab notebook; #2–#4 the Debt-3 calc notes; #5–#8 the Debt-1 calc notes; #9 the first consolidation, v1.0; #10 and #12 the popular articles; #11 the checkpoint; #13 conjugate special relativity; #14 the withdrawn soliton manuscript; #15 the skeptic review console. The toy-model note, papers/reciprocity-toy-models.md, came after the handoff. Documents maps each to its file.
Mathematical symbols are on Notation, cited works on References, and the status registers under Status.

Numbers and marks#

#1–#15. The artifact numbers of the documents carried over from claude.ai, listed under Using the glossary. See Documents.
0+1, 1+1, 2+1, 3+1 dimensions. A count of space dimensions plus one time dimension. The quantum mechanics of a few degrees of freedom is 0+1; the toy models are built in 1+1, where a compact continuous symmetry cannot break spontaneously; in 2+1-dimensional quantum gravity the momenta of a particle live on a curved space; the program’s world is 3+1. See The Mermin–Wagner–Coleman theorem and Curved momentum space.
3+1 presentation. #13’s construction in which the position and momentum polarizations share time, so that the dual light cone lies in time and momentum, with the maximum force c̃ as its slope. The fully covariant alternative, the four-dimensional Born map, has not been built. See Open: the two dual cones.
[D], [T], [P], [O], [V]; †, [S]. The provenance tags: derived in the program, taken from the established literature, postulated, open, and checked by machine. The citation marks: † for a reference recalled from model memory and not yet checked against its source, [S] for one retrieved by a live search. Forms such as [D + T], [D][V] or [D — structural] combine or qualify tags. See Provenance tags and citation marks and its section on combined and qualified tags.
✓. The handoff’s mark for a machine-checked result, where later documents write [V]. Flag 16 in review/wiki-build-flags.md notes one ✓, on the Debt-3 shortfall, with no script behind it. See The handoff document.
√N topological floor; Kibble ceiling. A chat-only argument that the net topological charge left by the soliton candidate’s phase transition sets a floor under its relic abundance, below a Kibble “ceiling”. It is dead: round 3 showed that Kibble’s count is a minimum, not a ceiling, and with the candidate retired the planned calculation was dropped (round-3 Decision 3). See Obituary: the √N topological floor (chat-only).

A#

Acceptance criterion 1. The referees’ standing demand for one explicit action, a toy model being enough, in which Born reciprocity is a genuine symmetry that the vacuum breaks, with the neutral metric η as the order parameter. Checkpoint #11 records it as met “in the referees’ wording” by model I with a bounded potential. A simulation with all fields dynamical, a derivation of the potential and the strong form of matter locality remain open, and an older clause, that η also select the hidden sector’s electric description, is not addressed. See Acceptance criterion 1.
Adjudication. The author’s written ruling on each finding of a blind review, made after the referee reports: disputed numbers are re-run in separate scripts, each finding is upheld, accepted or overturned, and the forecast committed before the round is scored. See The blind-review protocol.
Aligned point; flat aligned vacuum. The point at which the two frames of the bimetric potential coincide (𝕏 = 1). A flat vacuum there requires V(1) = T, and with the palindrome’s identity V(1) = 2T this forces T = 0 and V(1) = 0. See The vacuum-energy identity.
α_d ≈ 34 (alpha-d). The coupling the soliton candidate gave its hidden monopoles, 1/(4α), with α ≈ 1/137 the fine-structure constant. All three ways of fixing it are dead: Dirac quantization against our photon, killed in round 1; reciprocity acting as the modular S transformation, set aside as numerology; and hypothesis H, withdrawn with #14. It is distinct from the magnetic coupling of our own electromagnetism, which #11 also puts near 34 (flag 28 in review/wiki-build-flags.md queries #11’s formula for it). See Obituary: the coupling α_d ≈ 34.
Anchor; circular anchor. A value known independently of the paper being checked, such as a textbook identity or a published number, that a verification script must reproduce before its own numbers are trusted. A check that reproduces the paper’s own figure is circular: the soliton manuscript’s script anchored its monopole count to the previous draft’s figure and passed a wrong normalization. See Independent anchors.
Anti-de Sitter transition. The future event, favoured in published fits of quintessence with a negative-minimum potential, in which the effective vacuum energy turns negative, the expansion halts and contraction begins. #11 §10 cites these fits for the turnaround, which the program reads as the conjugate bounce. See Row 5: the fate of the expansion and anti-de Sitter space.
Appendix A. Collision. In HANDOFF.md, the code of the seven-test verification battery, now verify/battery.py; in checkpoint #11, the audit of the eleven founding suppositions. See The verification battery T1–T7 and Founding suppositions and their fates.
Arbitration (round 3). The adjudicator’s own recomputation of the numbers the round-3 referee disputed, run before the rulings: the Kibble normalization, the mass at which the monopoles would make up the dark matter, and the relic density of the light hidden fermion ψ. Its numbers were carried into the gate. See Round-3 arbitration and the referee’s constants.
Arithmetic, not the model. The rule that a verification script confirms the arithmetic of the model it encodes, not whether that model is the right physics. The soliton manuscript passed such a script with a wrong normalization, which only an independent review caught. See Verification checks arithmetic, not the model.
Assessment. Checkpoint #11’s closing judgement of the program in Lakatos’s terms (§15): the hard core intact after two forced corrections, the progressive signs, the degeneration risks and the near-term falsification exposure. Its verdict is that the program is a live research program, with the word “theory” held back. See Assessment: a live research program.
Asymmetric dark matter; Sakharov conditions; baryogenesis. Dark matter whose density is set by an excess of particles over antiparticles, as the density of ordinary baryons is. Making such an excess from a symmetric start needs the three Sakharov conditions: a process that violates the conserved number, violation of charge conjugation (C) and of charge conjugation and parity combined (CP), and a departure from thermal equilibrium. Baryogenesis, the making of the baryon excess, is the template for the program’s missing polarization-genesis. See Relic abundance mechanisms.
Attribution line. The line the program’s papers carry: “conjecture and direction, P.R.; derivations, counterexamples, verification, drafting, Claude (Anthropic).” See The collaboration.
Audit trail. Documents kept as the record of how the program reached its present state but superseded as references, such as the lab notebook, the first consolidation #9 and the withdrawn manuscript #14; the wiki cites them for history, not for current status. See Documents.
Auxiliary field. A field with no motion of its own. The shift symmetry rules this out for the momentum graviton X, which either propagates or does not exist. See Shift symmetry: X is never auxiliary.
Axion-like field. A field that is an angle: its couplings are unchanged when its value is shifted by a constant, apart from a small breaking that leaves a periodic potential, and the shift symmetry keeps it light. Axions are the standard example, and the program’s dark-energy field τ is of this kind, with the potential V₀[1 + cos(τ/f)]. See Axion-like fields and pseudo-Goldstone bosons.

B#

Baryon acoustic oscillations (BAO). The imprint of sound waves in the early universe’s plasma on the distribution of galaxies: a preferred separation that serves as a ruler at every later epoch. From it the Dark Energy Spectroscopic Instrument (DESI) measures distances and, by fitting a model, infers the dark-energy equation of state. See DESI baryon acoustic oscillations.
Benchmark. Collision. The scattering benchmark fixes conjugate matter’s self-scattering from the cores of dwarf galaxies and gives m_χ ≈ 70 MeV·α̃^{2/3}(σ₀/m ÷ 30 cm²g⁻¹)^{−1/3} (#11 §8). The soliton benchmark was #14 v3’s monopole mass of 3×10¹³ GeV, which round 3 found overproduced. See The scattering benchmark, Overproduction at the benchmark and Obituary: superheavy conjugate solitons.
Benchmark-conditional arithmetic. Numbers that #14 v3 computed at its withdrawn benchmark mass and that remain correct as arithmetic: the monopoles’ density and spacing, their self-scattering per unit mass, the counterfactual flux and the overclosure by W′ bosons. See Benchmark-conditional arithmetic.
Big Bang nucleosynthesis (BBN). The formation of the lightest nuclei, mostly helium-4 with traces of deuterium, helium-3 and lithium-7, in the first minutes of the hot early universe. The helium abundance measures the expansion rate at that time, and so the radiation content and the strength of gravity together. The lab notebook dates row 10’s optional step in G_eff “before BBN”, and at MeV masses the retired soliton candidate’s light fermion ψ would still have been freezing out during it. See Big Bang nucleosynthesis.
Bigravity dark matter. The published proposal of Babichev and collaborators, cited from model memory, that the massive spin-2 field of bimetric gravity is the dark matter; the lineage of the program’s X-condensate candidate. See Bigravity dark matter.
Bimetric gravity; Hassan–Rosen. Gravity with two dynamical metrics, each with its own dynamics, coupled by the ghost-free Hassan–Rosen potential, a sum of five terms with constant coefficients β₀ to β₄. About proportional backgrounds it has one massless and one massive spin-2 field. The program’s gravity is this theory with the second frame confined to a compact space. See Hassan–Rosen bimetric gravity and Constrained bimetric gravity.
Binder cumulant. A ratio of moments of an order parameter’s distribution, used in simulations to tell ordered from disordered phases; the toy-model note’s ordered run gives 0.667. See Monte Carlo: an ordered ℤ₂ phase.
Blind review. The program’s test of a manuscript: a fresh AI referee receives only the manuscript, checks its citations, re-runs its numbers and grades it A, B or C, after the author has committed a forecast of the outcome. Four rounds have run, three on the soliton manuscript #14 and one on the toy-model note. See Blind review.
Born approximation; Born regime. Collision. The weak-coupling approximation of scattering theory, valid when the coupling is weak compared with the ratio of the mediator’s mass to the particle’s. The name is Max Born’s, but the approximation has nothing to do with Born reciprocity. The lab notebook derives the gated scattering law in it and calls it marginal at its benchmark coupling. See Self-interacting dark matter.
Born connection. The rule for comparing vectors at neighbouring points of phase space that respects all three structures ω, η and H of a Born geometry; a theorem of Freidel, Rudolph and Svoboda shows that, under its conditions, there is exactly one. Whether a unique compatible connection still exists when only ω and H are fundamental is open. See The Born connection.
Born duality; broken Born duality. Freidel, Leigh and Minic’s name for Born reciprocity. “Broken Born duality” is their phrase for a preferred polarization; they made η dynamical but wrote no potential for it, and reading the breaking as spontaneous, with η as the order parameter, is the program’s addition. See Broken Born duality.
Born geometry. Phase space carrying three compatible structures, the symplectic form ω, the neutral metric η and the generalized metric H, whose pairwise products I, J and K multiply like split quaternions; the name is Freidel, Leigh and Minic’s. See Born geometry and The structures ω, η, H and the split-quaternion algebra.
Born length. The reference length λ that, with the momentum ε = ℏ/λ, puts position and momentum on a common scale. In #13’s conjugate special relativity it sets the maximum force c̃ = ℏc/λ², and #13 sets it equal to the Planck length in an untagged step. See The Born length λ and The maximum force.
Born map (3+1 and four-dimensional). The exchange of position and momentum in #13. The 3+1 version exchanges space with momentum and leaves time shared; the four-dimensional version would also exchange time with energy, and it has not been built. See Open: the four-dimensional Born map and dual dynamics.
Born reciprocity; Born rotation; ρ (rho). The quarter-turn ρ: (x, p) → (p, −x) of phase space, which leaves the rules of quantum kinematics unchanged and which the Fourier transform carries out on wavefunctions; applied twice it is the half-turn (x, p) → (−x, −p). The program’s hard core holds that it is an exact symmetry of the laws that the vacuum breaks. See Born reciprocity ρ.
Born sigma model. A sigma model in which Born geometry is the target structure and the polarization is chosen by gauging (Marotta and Szabo); related to, but not the same as, the program’s coset toy model. See Coset and hyperbolic sigma models.
Born’s answer. The program’s answer to Born’s question: momentum-space geometry is dynamical, carried by X, a massive spin-2 field that changes sign under reciprocity, with two free parameters and no vacuum energy from its interaction potential. See Born’s answer: momentum space gravitates.
Born’s debt. The lab notebook’s name for the missing field equation of the phase-space metric H, “Born’s 88-year debt”; later Debt 1. See The three debts.
Born’s question. Why physics singles out position when quantum kinematics treats position and momentum as equals: interactions are local in position, and general relativity curves space-time while leaving the space of momenta flat. Max Born raised it in 1938. See Born’s question.
Bose star; kinetic condensation. A dense, coherent ground-state core that forms in a halo of wave dark matter when the waves scatter into the lowest-energy states, a kinetic condensation that Levkov, Panin and Tkachev worked out for gravity. The Debt-3 notes call such a core a soliton. See Wave kinetics and Bose-star formation.
Bosenova; attractive condensate; critical mass. An attractive condensate is a Bose star whose particles also attract one another. Above a critical mass M_crit it collapses, throws off part of its mass as fast waves in a burst called a bosenova, and the remnant regrows. In the dead Scenario A this cycle would have drained the ultra-faint dwarf galaxies of their dark matter. See Attractive condensates: critical mass and the bosenova.
Boulware–Deser ghost. The extra negative-energy mode that a generic nonlinear mass term for a spin-2 field brings back. The special de Rham–Gabadadze–Tolley and Hassan–Rosen potentials keep it out, and the metric-tier potentials of the tuning test have it. See The Fierz–Pauli mass term and the Boulware–Deser ghost.
Bounded potential V_b. The repaired ρ-preserving potential of model I: the naive potential divided by a normalizing factor, so that it stays between −μ and 0. It leaves the vacuum stable with the metric H free to vary, keeps one flat direction that no symmetry protects, and is put in by hand rather than derived. See The bounded potential V_b.
Branch. Collision. Branch R is the theory under the original P2: general relativity plus one model of self-interacting dark matter (#5 §B). Branch (i) and Branch (ii) are the two mass ranges of the ultra-faint-dwarf endpoint of Scenario A (#4): the bulk of the wave island, where the condensate is a mass drain, and lighter masses that observations already exclude. The palindromic, or interchange-symmetric, branch is the family of bimetric potentials with βₙ = β₄₋ₙ (#8). See Original P2, Obituary: Scenario A and The palindromic branch.
Broken-Born program (BBT). The research program this wiki describes, developed by Paul with Claude since September 2026: Born reciprocity is taken to be an exact symmetry of the laws that the vacuum breaks spontaneously, and the consequences are followed into gravity, dark matter, dark energy and electric–magnetic duality. It calls itself a Lakatosian research program, not a theory; the lab notebook’s title says Broken-Born Theory. See The Broken-Born program and The research program.
Bullet Cluster. A pair of colliding galaxy clusters whose separated dark and visible matter limit how strongly dark matter scatters off itself. #11 §8 calls conjugate matter “Bullet-Cluster-safe”: it falls like ordinary matter, and its self-interaction is off at cluster velocities. See The Bullet Cluster.

C#

Calc notes. The seven working notes #2–#8, written to close the lab notebook’s debts: #2–#4 on Debt 3, whether dark matter forms velocity streams, and #5–#8 on Debt 1, the field equation of momentum-space geometry. They are final for their own scope and kept as the audit trail, and checkpoint #11 now states their results. See The Debt-3 calc notes (#2–#4) and The Debt-1 calc notes (#5–#8).
Cannibal dark matter. A dark sector whose particles cannot annihilate into anything lighter, so that number-changing self-interactions set its abundance: for example, three particles scatter into two and the rest mass of the third becomes heat. The lab notebook names the “cannibalism problems” of such a sector as the reason particle χ cannot get its abundance from thermal freeze-out. See Relic abundance mechanisms.
Canonical commutator. [x, p] = iℏ, the rule that position and momentum do not commute, which rules out states sharp in both. #11 reads it as requiring any world with local physics to select a polarization. See The canonical commutator and the uncertainty principle.
Charge lattice; duality frame; Lagrangian sublattice. The lattice of allowed electric and magnetic charges. The Dirac–Schwinger–Zwanziger (DSZ) pairing makes it a symplectic space, mutually local charges form a Lagrangian sublattice, and choosing which charges count as electric, a duality frame, is choosing a polarization of charge space. See The symplectic charge lattice.
Chat-only. Said of a result that exists only in the original claude.ai conversation, recorded in HANDOFF.md §4 and derived in no document. Such results have the status conjecture, the handoff calls some of them “conjecture tier”, and their page titles end “(chat-only)”. See Conjectures: chat-only and popsci-only claims.
Checkpoint. Document #11, papers/broken-born-checkpoint-v2.md, now at version 2.2: the program’s paper-length statement of everything it has derived, predicted, retracted and left open, and the current reference for the whole program. Its first version was #9 (v1.0). See The checkpoint: #9 to #11 v2.2.
Claim tiers. Checkpoint #11’s ranking of its own statements by how much trust each deserves: Tier 1, explicit algebra checked by machine; Tier 2, established literature; Tier 3, the program’s new structural physics, to which #11 gives a prior of ~50–80% per claim pending expert review. Negative results are the most reliable Tier-3 items. See Claim tiers and selection bias.
Classicality theorem. The result that dark matter coupled strongly enough to clump in velocity must be so light that each quantum state holds an enormous number of quanta, so that it behaves as a classical wave: collective velocity dynamics and classical-particle dark matter exclude each other. It splits dark matter into the particle island and the wave island. See The classicality theorem and the particle island.
Cliff. The lab notebook’s exponential cutoff of the self-interaction cross-section at the gate velocity v*. Once the gate’s mechanism was found the program kept only the knee, and the shape of its tail became open. See The gated scattering law σ_T(v).
Cold stellar streams. Long, thin trails of stars pulled off globular clusters or small galaxies by the Milky Way’s tides, which lumps of dark matter disturb as they pass. The lab notebook’s withdrawn row 3 predicted correlated ripples along them. See Halo-substructure probes and Obituary: velocity-space granularity in halos.
Collapse-powered expansion. The founding supposition that the gravitational collapse of the conjugate universe drives the acceleration of ours. It is dead twice: the early heuristic translation rule required dark energy with w = −2, which data exclude, and the corrected duality dictionary makes collapsing conjugate matter slow our expansion as ordinary matter does. See Obituary: conjugate collapse powers our expansion.
Compatibility corollaries. Three consequences of the compatibility theorem’s answer H = diag(g, g⁻¹): det H = 1, which the program reads as the constancy of Planck’s constant; no antisymmetric B-field block; and a momentum metric fixed as the inverse of the position metric, g̃ = g⁻¹, the slaved momentum metric. The last contradicted the program as it then stood and forced the change of postulate to P2′. See Corollaries: unimodularity, no B-field, slaved momentum metric.
Compatibility theorem. With the symplectic form ω and the neutral metric η both held fixed, the only positive metrics H compatible with both are H = diag(g, g⁻¹). The statement is Freidel, Leigh and Minic’s; the short block proof and its machine check, battery test T1, are the program’s, and round 3 re-derived it independently. It showed that holding η fixed leaves the program with no content of its own. See The compatibility theorem.
Complex structure (I). The operator I = ω⁻¹H built from the symplectic form and the generalized metric; it squares to −1 and generates the Born rotation of postulate P3. On the modular field it is written I[Z]. See The structures ω, η, H and the split-quaternion algebra and P3: a reciprocity-invariant action.
Condensate. Collision. Four things: the Bose-star condensate of χ that gated attraction drives on the wave island (#3, #4); the X-condensate, a coherent oscillation of the momentum graviton proposed as the dark matter (#11 §12); the monopole condensate of the dual-superconductor picture of confinement (#11 §11.2); and the condensed oscillator levels of model II, the complex Grosse–Wulkenhaar (GW) model (toy-model note §3–§4). No document relates the first two. See The wave island, The X-condensate candidate, The dual superconductor and Quantum restoration in the complex model.
Conditional pass. The verdict of the tuning test: the potential that gives X its mass carries the Boulware–Deser ghost in second-order (metric) variables and is ghost-free in first-order (frame) variables, the formulation the calc notes argue is the natural one. The passing class was selected rather than derived. See The verdict: a conditional pass.
Confabulation. Fluent statements by an AI model that are false, such as a wrong citation or an invented number: the failure mode the program’s tags, machine checks and pre-registered reviews exist to catch, and the skeptic console’s gloss for verdict C. See The collaboration and Method.
Conjugate. Collision. In the program’s own terms, the momentum-side counterpart of something ordinary: conjugate matter, the conjugate universe and its bounce, conjugate special relativity, conjugate monopoles. In established physics, position and momentum are conjugate variables, and charge conjugation, as in “hidden charge conjugation”, is an unrelated symmetry. See The conjugate universe and Conjugate matter and the velocity gate.
Conjugate bounce. The far-future turnaround of our expansion read in the conjugate description: because our scale factor and the conjugate one are reciprocals, the moment ours is largest is the moment the conjugate universe is smallest and rebounds, one event with two descriptions. Its premise, a negative V(τ), conflicts with the potential as written (flag 27 in review/wiki-build-flags.md). See The turnaround as the conjugate bounce.
Conjugate matter (χ). Matter in the momentum-polarized representation, the counterpart of ordinary matter with the roles of position and momentum exchanged. It gravitates exactly like ordinary matter, no gauge force of ordinary matter acts on it, and its self-interaction acts only between particles of nearly equal velocity, through the velocity gate. As particles it is one of the two remaining dark-matter candidates. See Conjugate matter and the velocity gate and The χ-particle candidate.
Conjugate monopoles. Magnetic monopoles, or other topological solitons, of the momentum-polarized sector. As the explanation of why our sector shows none, the idea is dead; the statement that they would gravitate if they exist stands. See Conjugate monopoles as ontology and Obituary: conjugate monopoles explain the null result.
Conjugate special relativity. #13’s transcription of special relativity into the momentum polarization: a second light cone whose invariant speed is a maximum force, force boosts, force dilation, an invariant length, and free fall as the dual state of rest. It is alive but unreviewed, nothing in it is machine-checked, and #11 does not mention it. See Conjugate special relativity.
Conjugate universe; conjugate frame; dual frame. The momentum-space description of our own universe: one physical state with two descriptions, related as a waveform is to its spectrum and synchronized rather than causally linked. It began as a founding supposition of a second universe coexisting with ours. See The conjugate universe: one state, two descriptions.
Consistency islands; forced convergence. Calc note #7’s terms for “the unique known consistent structure” to which a structural test restricted the program’s geometric sector, such as the Hassan–Rosen class at the tuning test; #11 §15 counts the repeated “forced convergence onto consistency islands” as a progressive sign. Where #11 §7.1 drops the word “known”, flag 7 in review/wiki-build-flags.md points to #6 §3’s “exactly one known consistent structure”. Consistency islands are not the particle and wave islands. See Assessment.
Constrained bimetric gravity; predictive truncation. The picture the tuning test leaves: Hassan–Rosen bimetric gravity whose second frame is the polarization frame, confined to the compact space Λ(d) of position–momentum splittings, ten-dimensional at d = 4. The massless combination of the two spin-2 fields is the ordinary graviton, the massive one is X, and the light direction is τ. Calc note #7 calls it a predictive truncation of bimetric theory. See Constrained bimetric gravity.
Cosmic microwave background (CMB). The thermal radiation released when the early universe became transparent, at recombination, now arriving at microwave wavelengths with a blackbody spectrum. Small differences in its temperature across the sky preserve the sound waves of the early plasma and measure the densities of ordinary and dark matter, the ruler of baryon-acoustic-oscillation surveys and N_eff. Planck 2018’s measurement of N_eff bounded the retired soliton candidate’s dark radiation, and row 10 names a planned experiment, CMB-S4, as its probe. See The cosmic microwave background.
Cosmological constant Λ; ΛCDM. A constant term in Einstein’s equations that acts as an energy density of empty space, the simplest form of dark energy, with equation of state w = −1 exactly; ΛCDM, the standard cosmological model, is a cosmological constant plus cold dark matter. It is the standard expectation of rows 4 and 5, and the program replaces it with the field τ. See The cosmological constant Λ.
Cosmological-constant problem. Quantum field theory predicts a vacuum energy far above the value the accelerating expansion indicates, and no accepted mechanism explains the gap. The program’s vacuum-energy identity concerns only the spin-2 interaction potential and does not by itself address it. See The cosmological-constant problem.
Cosmological constraint. a·ã = 1: holding the symplectic form fixed fixes the size of a comoving phase-space cell, so our scale factor a and the conjugate scale factor ã are reciprocals, as stretching a waveform compresses its spectrum. The documents identify it with the |Z| = 1 circle of the modular field, an identification queried as flag 23 in review/wiki-build-flags.md. See The cosmological constraint a·ã = 1.
Counterfactual flux. The monopole flux the soliton candidate would have had if its monopoles carried magnetic charge under our electromagnetism: far above the Parker bound, which shows why its hidden sector had to be separate from ours. See Benchmark-conditional arithmetic.
Covariance. A weaker relation than a symmetry. A map is a symmetry of an action when it takes every allowed field to an allowed field with the same action, and only a covariance when the action keeps its value after being rewritten in new variables. In model II the duality is a symmetry for complex fields and only a covariance for real ones, which is how a preference between the real model’s vacua can arise. See Complex versus real fields: symmetry versus covariance.
CPL parametrization; w₀, wₐ; thawing corridor. The Chevallier–Polarski–Linder form w(a) = w₀ + wₐ(1 − a) of the dark-energy equation of state, with a the scale factor: w₀ is the value today and a negative wₐ means that w has been rising as the universe expands. Thawing models lie near a line in the w₀–wₐ plane, which the program writes as the thawing corridor wₐ ≈ −1.5(1 + w₀) without a reference; a fit with w₀ > −1 and w₀ + wₐ < −1 describes a crossing of w = −1, the shape the second data release of the Dark Energy Spectroscopic Instrument favours. The corridor itself lies in that region, so a fit there does not by itself show that dark energy crossed −1 (flag 43 in review/wiki-build-flags.md). See The CPL parametrization w(a) = w₀ + wₐ(1 − a) and Thawing and freezing quintessence.
Criterion. Collision. Acceptance criterion 1 is the referees’ demand for an explicit symmetric action; S0–S5 are the toy models’ success criteria; the mean-field criterion is Debt 3’s threshold for stream formation; and the program’s health criterion requires X’s potential to land in the de Rham–Gabadadze–Tolley and Hassan–Rosen class. See the entries for each, and dRGT massive gravity.
Curved momentum space. Literature in which the space of momenta has a geometry of its own: Snyder’s quantized space-time, momenta on a curved space in 2+1-dimensional quantum gravity, and relative locality. The program’s own version is the momentum graviton X. See Curved momentum space.
Cusp–core problem. Simulations of collisionless cold dark matter predict steep central density peaks (cusps) where many dwarf galaxies show flat cores; a self-interaction, wave dark matter or gas blown out by supernovae can flatten them. The program fixes conjugate matter’s self-scattering by fitting such cores. See Dwarf galaxies: cores and ultra-faint dwarfs.

D#

Dark energy. Whatever makes the expansion of the universe accelerate; in the standard cosmological model, a cosmological constant. The program identifies it with the field τ, the angle that sets how the vacuum divides phase space into position and momentum, which may weaken but never become phantom. Data Release 2 (DR2) of the Dark Energy Spectroscopic Instrument (DESI) leans against that requirement, so the sector is under real pressure. See Dark energy.
Dark matter. The mass detected only through its gravity, in the orbits of stars and gas, the motions of galaxies in clusters and the bending of light, and which emits and absorbs no light of its own. The program offers two candidates, χ particles and an X-condensate. See Dark matter.
Dark-matter halo. The extended cloud of dark matter in which a galaxy or a galaxy cluster sits; it outweighs the visible stars and gas and sets their orbits. See Halo astrophysics.
Dark radiation; N_eff; ΔN_eff. N_eff is the effective number of light neutrino-like species, which nucleosynthesis and the cosmic microwave background both measure; extra light species add to it, an excess written ΔN_eff and called dark radiation. In row 10 a closed dual space would act as negative dark radiation; the hidden photon of the retired soliton candidate would have added positive dark radiation. See The radiation era: thermal history and N_eff, Big Bang nucleosynthesis, the cosmic microwave background and The hidden sector’s thermal history.
Dark-sector candidates. The program’s answers to what dark matter is made of: χ particles or an X-condensate, both alive and both open, sharing one unexplained abundance ratio, Ω_χ : Ω_b = 5.4 : 1. A third answer, superheavy solitons, was retired on 2026-10-19. See Dark-sector candidates.
de Sitter space; anti-de Sitter space. The spacetime of a universe expanding at a constant rate under a positive cosmological constant; with a constant dark energy, standard cosmology expands forever toward it. Anti-de Sitter space is its counterpart for a negative cosmological constant. See De Sitter space and Row 5: the fate of the expansion.
Dead stays dead. The rule that a claim killed by calculation, data or review is reported prominently, in an obituary of its own, and is not revived. See Negative results and dead claims and The graveyard.
Debt 1, Debt 2, Debt 3. The lab notebook’s three most severe open problems, which it named debts: the field equation for momentum-space geometry (Debt 1), the origin and shape of the velocity gate (Debt 2), and whether the gated interaction makes dark matter gather into streams of shared velocity (Debt 3). Debt 1 was closed in structure; Debt 2’s mechanism was found and its shape left open; Debt 3 closed negative. See The three debts.
Decisions (round 3). The four decisions taken after review round 3: strict sector separation (Decision 1), the soliton candidate retired (2), the √N floor dropped (3) and the toy Lagrangian made the next task (4), together with two lessons for the method. See Round-3 decisions and lessons.
Definition of done. scripts/check.sh, which runs the verification scripts and the wiki check; work is not finished until it passes, and no check may be weakened to make it pass. See The gate: scripts/check.sh.
Degeneration flag; degeneration risk. Calc note #3’s label for an option the framework allows but does not require, such as velocity streams tunable across about ten orders of magnitude in Scenario B. Checkpoint #11 §15 lists such options among its degeneration risks, the signs that a research program is absorbing failures rather than predicting. See Scenario B and Assessment.
Diagnostic row. A row of the predictions table that sorts dark matter into one branch or another instead of being able to kill the program: rows 3 and 11. See Predictions and kill conditions.
Dimension-five operator; Planck-suppressed adjoint mixing. The operator Φ^a F^a B/M_*, which mixes a hidden photon with our hypercharge field once the hidden scalar Φ takes its vacuum value v, giving a kinetic mixing ε ~ v/M_*. The operator exists in the literature, but #14 v3’s coefficient of order one at the Planck scale had no source, and the estimate is dead. See Obituary: Planck-suppressed adjoint mixing.
Dirac quantization. The rule that a magnetic monopole can exist in quantum mechanics only if the product of its magnetic charge with every electric charge is a whole-number multiple of a fixed constant, e·g ∈ 2πℤ in the checkpoint’s normalization. A weakly coupled force therefore has strongly coupled monopoles. See Dirac quantization and the DSZ pairing.
Direct detection. Experiments that look for dark-matter particles striking atomic nuclei in shielded underground detectors, or for dark matter made in particle collisions; both need a coupling to ordinary matter besides gravity. Row 7 predicts a permanent null, because postulate P4, read strictly, lets no such coupling cross between the two sectors of matter. See Row 7: a permanent null in direct detection.
Double field theory (DFT). String theory’s doubled geometry: the closed string’s low-energy fields written on a space in which each coordinate has a dual partner, with a generalized metric that preserves a neutral metric η, the antisymmetric Kalb–Ramond B-field and a section condition. For the program it is the contrast case: doubling with η gives the metric an antisymmetric partner, doubling with ω a second graviton. See Double field theory and the generalized metric.
Dual. Collision. In the program’s own terms, “dual” marks the momentum-side counterpart of an ordinary object: the dual frame, the dual cone, dual stress, dual inertia, the dual diffeomorphisms of X. In established physics the word keeps its other meanings: electric–magnetic duality and the dual superconductor exchange electric with magnetic. See Duality, below.
Dual cone; two causal cones. In #13, the light cone of momentum space, which bounds the rate of change of momentum, |dp/dt| ≤ c̃, alongside the ordinary cone that bounds speed. #13 uses two different versions of it, an open inconsistency. See Two causal cones and Open: the two dual cones.
Dual diffeomorphisms. Local shifts of the momentum graviton, δX_μν = ∂₍μλ_ν₎, a second copy of the linearized coordinate changes of general relativity, which make X a second graviton-like gauge field. See Dual diffeomorphisms: a second graviton.
Dual dynamics. The field equations of the momentum polarization (“their Maxwell, their field theory”), which do not exist: only #13’s dual kinematics has been written, and its dual second law stays conjecture-tier until they do. See Open: the four-dimensional Born map and dual dynamics.
Dual equivalence principle. A chat-only open question: whether the second gravitational charge, dual stress, is tied to the invariant length of conjugate quanta. See Two gravitational charges and the conjugate field equations (chat-only).
Dual gravity term; step in G_eff. The lab notebook’s term for the conjugate side’s gravity in the cosmological equations: it adds to the effective Planck mass a piece that grows toward the past as a⁻⁶, which changes the effective strength of gravity G_eff before nucleosynthesis. It is an optional imprint, tested by row 10. See The duality dictionary and Row 10: an early step in G_eff.
Dual inertia; dual-inertial frame; dual second law. In #13, motion at a constant rate of change of momentum, dp/dt: zero force, which is free fall in general relativity, is the dual state of rest, and a constant force is uniform dual motion. #13 marks the dual second law built on this conjecture-tier. See Dual inertia: free fall as rest.
Dual interval; dual Lorentz group; force boost. #13’s interval ds̃² = c̃²dt² − dp² and the transformations that preserve it. A force boost carries an observer under no force to one under a constant force, as a Lorentz boost relates observers at constant velocity. See Force boosts and force composition.
Dual kinetic energy. Kinetic energy in the conjugate description, which by the duality dictionary acts on our expansion like a cosmological constant. The lab notebook names it the natural source of dark energy but implements dark energy as τ’s potential energy, and no document derives one from the other. See Open: dual kinetic energy versus τ’s potential.
Dual proper time; force dilation; momentum-spread contraction. In #13, a system of the conjugate polarization under a large sustained force evolves slowly, by the time-dilation formula with force in place of velocity, and a forced system’s spread in momentum contracts. Which physical clocks respond is open. See Force dilation.
Dual stress. The quantity T̃ through which matter couples to the momentum graviton X, as stress-energy is for the ordinary graviton; it is built from derivatives along the momentum directions. The calc notes define it in words and give no formula. See Dual stress T̃.
Dual-stress enhancement. The unexplained gap between conjugate matter’s strong self-scattering, which #11 calls nuclear-scale, and the gravitational-strength coupling of ordinary matter to the same carrier X. It is open problem 5 (OP5), which #11 calls the “main open quantitative item” of the conjugate sector. See Open: the dual-stress enhancement (OP5).
Dual superconductor; confinement. Confinement is the observed fact that quarks are never found in isolation. In the dual-superconductor picture of ’t Hooft and Mandelstam, the vacuum of the strong interaction holds a condensate of magnetic monopoles that squeezes the color-electric field between quarks into strings. See The dual superconductor.
Duality. Collision. Born duality is Freidel, Leigh and Minic’s name for reciprocity. Electric–magnetic duality exchanges electric and magnetic descriptions; its proposed exact quantum form is S-duality, and string theory’s T- and U-duality are the others #11 §11.3 compares with. Seiberg duality supplies magnetic quarks. The Langmann–Szabo duality exchanges positions and momenta in noncommutative field theory. Scale-factor duality relates our scale factor to the conjugate one, and the duality dictionary translates fluids between the two descriptions. See Broken Born duality, S-duality and Montonen–Olive, Noncommutative field theory and the Langmann–Szabo duality and Scale-factor duality.
Duality dictionary. How energy in the conjugate description acts on our expansion: a fluid with equation of state w̃ there acts like one with w_eff = −w̃ here, so conjugate kinetic energy acts like a cosmological constant and dust like dust. It replaced an earlier heuristic rule, w_eff = −2 − w̃, which is superseded. See The duality dictionary w_eff = −w̃.
Dwarf galaxies. Small, faint galaxies, many of them satellites of the Milky Way, whose mass is mostly dark matter. The brighter classical dwarfs show the flat cores that fix conjugate matter’s self-scattering; the ultra-faint dwarfs, the densest and most dark-matter-dominated systems known, falsified Scenario A. See Dwarf galaxies: cores and ultra-faint dwarfs.
Dynamical friction. The drag a massive body feels from the gravitational wake it raises in a sea of lighter particles, which makes globular clusters sink toward the centre of a dwarf galaxy. The lab notebook’s withdrawn row 4 predicted it suppressed in condensed cores. See Halo-substructure probes and Obituary: Fornax friction suppression (old row 4).
Dyon. A particle carrying both electric and magnetic charge. See Dirac quantization and the DSZ pairing.

E#

Electric–magnetic duality. The symmetry of Maxwell’s equations under exchange of the electric and magnetic fields: exact in empty space, and extended to matter only if magnetic charges exist alongside electric ones. Its proposed quantum form is S-duality. See Electric–magnetic duality and charge lattices.
Electric sublattice (clause). The part of acceptance criterion 1, in HANDOFF.md §2 and #14’s wording, that asks η also to select the hidden sector’s electric description. The toy models do not address it. See Acceptance criterion 1.
Elementary symmetric polynomials. The sums eₙ of all products of n distinct entries of a list. Applied to the eigenvalues of the matrix √(g⁻¹f), they are the building blocks of the ghost-free bimetric potential. Power sums such as p₄ can be written in terms of them only nonlinearly, which battery test T7 uses. See Elementary symmetric polynomials.
Entropy dilution; early matter domination. Thinning of relics made after reheating by a late release of entropy into the plasma, for example by the decay of heavy particles that dominated the universe for a time (early matter domination). The superheavy soliton candidate could have survived only with a free dilution factor of this kind, which the program rejected. See The relic yield Y = n/s and entropy dilution.
Equal Planck masses. The Planck mass of a metric sets how strongly it responds to matter. Reciprocity forces the program’s two spin-2 frames to have equal Planck masses, so ordinary matter feels X at gravitational strength, and the known late-time stability of a heavy spin-2 field, which assumes the second Planck mass much smaller, does not apply: stability is open. See Spectrum, parameters and reciprocity parity, Planck units and the two Planck masses and Open: stability at equal Planck masses.
Equation of state. The ratio w of a cosmic fluid’s pressure to its energy density: w = −1 for a cosmological constant, w = 0 for dust, w = +1 for a stiff fluid. See Quintessence and the equation of state.
Equivalence principle; universality of free fall. The statement that gravity acts on every body alike. In its weak form, the universality of free fall, a body’s path does not depend on what it is made of; in Einstein’s form, a small freely falling laboratory is an inertial frame, and uniform acceleration cannot be told apart from a uniform gravitational field. General relativity builds it in by coupling all matter to one metric, and postulate P4 extends it to conjugate matter, which therefore falls and bends light like ordinary dark matter. See The equivalence principle: free fall and local inertial frames.
Equivalence principle as dual relativity. #13’s reading of general relativity’s equivalence principle, the equal footing of all freely falling frames, as the principle of relativity of the momentum polarization: in dual kinematics, rest means feeling no force. See The equivalence principle as dual relativity.
Euclidean skeleton; Lorentzian dressing. The compatibility theorem, the parametrization of the Siegel domain and the chain that makes X massive are proven for positive-definite metrics (the skeleton). Carrying them over to the signature of spacetime, in which time enters with the opposite sign to space (the dressing), is open problem 3 (OP3). See Open: Lorentzian dressing of the Euclidean skeleton (OP3).
Exclusion conditions; requirements (i)–(iii). #14’s list of observations that would kill the soliton proposal, and its list of additions that consistency forced on it: a light hidden doublet fermion, a colder hidden sector and an unbroken hidden U(1). See The soliton candidate (retired) and Obituary: superheavy conjugate solitons.
External clock. The handoff’s name for the data releases of the Dark Energy Spectroscopic Instrument, whose data can kill the dark-energy sector or the whole framework; the third release is the next. See DESI baryon acoustic oscillations and Timeline.

F#

Falsification exposure. #11 §15’s term for how directly and how soon data can kill the program; it names rows 1, 4 and 7 of the predictions table as near-term. See Assessment.
Field content of the broken vacuum; moduli. The fields the geometry leaves once the vacuum has chosen a polarization: the metric, X, the ten moduli (independent directions) of the Lagrangian Grassmannian at d = 4, τ among them, and matter. Whether inverse-Higgs constraints remove the nine moduli besides τ is open. See Open: field content of the broken vacuum.
Fierz–Pauli mass term. The only mass term that gives a free spin-2 field a mass without a ghost, proportional to Tr(h²) − (Tr h)²; the program’s metric-tier potentials lack the −(Tr h)² term. See The Fierz–Pauli mass term and the Boulware–Deser ghost.
Fifth-force safety. The requirement that a new field produce no detectable extra force between ordinary bodies. X is safe by its short range, although ordinary matter feels it at gravitational strength; τ is safe because, as an approximate Goldstone field, it couples to matter only through its rate of change. See Safety by range: X and ordinary matter, Fifth-force safety of τ and, for the form searches test, Yukawa forces and their range.
First-order phase transition. A transition that proceeds by bubbles of the new phase forming, growing and colliding. In the early universe the collisions and the sound waves they leave make a random background of gravitational waves, whose frequency today is set by the transition’s temperature and duration. See Gravitational waves from phase transitions.
Flag (n). A numbered item in review/wiki-build-flags.md, the list of suspected errors in the source documents found while this wiki was built. The wiki quotes a flagged statement as written and points to its item, and each item awaits Paul’s ruling. Unrelated to the degeneration flag. See Timeline.
Force composition. #13’s law F₁ ⊕ F₂ = (F₁ + F₂)/(1 + F₁F₂/c̃²), under which forces combine like relativistic velocities and no combination exceeds the maximum force c̃. See Force boosts and force composition.
Forcing chain. The argument of #11 §7.1 that leaves X one option, a mass: the shift symmetry rules out an auxiliary X, the dual diffeomorphisms make it a second graviton, the multi-graviton no-go theorem excludes a second massless graviton that interacts, and the signature obstruction excludes dropping its gauge symmetry. It replaced an earlier three-way question: healthy, auxiliary or a ghost. See Why X must be massive.
Fornax timing problem. The Fornax dwarf galaxy keeps globular clusters that dynamical friction should have drawn to its centre. The lab notebook’s withdrawn row 4 explained this by suppressed friction in condensed cores, a prediction that is dead. See Obituary: Fornax friction suppression (old row 4).
Founding image. The program’s starting picture: dark matter breaking up into a few streams of shared velocity, so that it clumps in momentum space rather than in position. Debt 3 found this impossible for particles, fatal where it would be mandatory for waves and optional elsewhere; it is dead as dynamics. See Obituary: velocity clumping, the founding image.
Founding suppositions. The eleven ideas P.R. brought to the program at its start, each audited with its fate in #11 Appendix A: alive, transformed, promoted to theorem, split, already established physics, or dead. See Founding suppositions and their fates.
Fourier transform. The exact, reversible map between a quantum state’s position description and its momentum description, the same operation that turns a sound’s waveform into its spectrum. Applied once it carries out Born reciprocity; applied twice it reflects x → −x. See The Fourier transform as a phase-space rotation.
Frame. Collision. A frame, or vielbein, is a set of local reference axes from which a metric is built, as in the frame tier; a duality frame is a choice of which charges count as electric; the dual or conjugate frame is the momentum-space description of the universe; a force-free, or dual-inertial, frame is #13’s state of rest; and the polarization frame E₀[J] is the second frame of the program’s bimetric potential. See the entries for each.
Frame tier; metric tier. Two ways of writing the potential that gives X its mass: from frames, first-order variables, or from metrics, second-order variables. The metric tier carries the Boulware–Deser ghost, a failure checked by battery tests T4 and T7; the frame tier lands in the ghost-free Hinterbichler–Rosen class by construction, an argument with no machine check. See The frame tier: the symplectic vielbein and The metric tier fails twice.
“Framework does no work”. The referees’ objection over rounds 1–3, stated most fully in round 3, that nothing numerical in the soliton dark-matter proposal depended on Born reciprocity. It made an explicit symmetric model the next task, and the toy models answer it only in part. See The ‘framework does no work’ critique.
Freeze-out; freeze-in. Two ways a relic density is set: a species in equilibrium with the hot plasma annihilates until the expansion outruns its annihilation (freeze-out), or a species is produced slowly from a plasma it never joins (freeze-in). See Thermal freeze-out and Relic abundance mechanisms.
Friedmann equation; minisuperspace; lapse. The Friedmann equation ties the expansion rate of a homogeneous universe to its energy density. Minisuperspace is gravity reduced to the scale factor a(t), with the freedom to choose the time coordinate kept as one function, the lapse. The program writes its cosmology in this form, with a second, conjugate scale factor. See Friedmann cosmology and minisuperspace.
Frozen-H reduction. Model I with its metric field held at H = 1, which leaves a two-dimensional spin model of the polarization angle; the toy-model note’s Monte Carlo simulates only this reduction, and a simulation with H dynamical is open. See The frozen-H reduction and Open: a Monte Carlo with H dynamical.
Fuzzy dark matter. Wave dark matter so light that its de Broglie wavelength reaches the size of a small galaxy’s core. Ultra-faint-dwarf kinematics and the Lyman-α forest bound its mass from below, which sets the wave island’s lower edge. See Bounds on fuzzy dark matter.

G#

Gate, the. Collision. In the physics, the velocity gate (below). In the method, scripts/check.sh, the check that must pass before work is called finished. See The velocity gate and The gate: scripts/check.sh.
Gate mechanism; fiber overlap. The program’s derivation of the velocity gate: two particles of conjugate matter interact by exchanging the heavy momentum graviton X, which acts as a contact interaction, and only where their wavepackets overlap along the momentum fibers. A χ quantum’s finite width μ along those fibers cuts off its interaction at large relative momentum, as a nucleus’s size cuts off its scattering at large momentum transfer. The derivation is structural. See The gate mechanism: X exchange over fiber overlap.
Gate open; gate narrow; broad gate; narrow gate. The two regimes of the gated interaction. With the gate open, or broad (halo dispersion σ ≲ v*), most pairs in a halo are inside the gate, as in dwarf galaxies; with the gate narrow (σ > v*), as in the Milky Way and clusters, only particles moving together take part, and the wave-island condensation rate falls by the power law (v*/σ)⁴. See The gated condensation rate Γ_self and The mean-field criterion.
Gate shape. Whether the gate cuts off as a Gaussian or with a power-law tail. It depends on how X propagates along the momentum fibers and on the profile of a conjugate quantum, neither of them computed; it is open problem 4 (OP4), and it is observable in the tail of the knee. See Open: the gate shape (OP4).
Gated Vlasov model. The simplified description of dark matter used in Debt 3: a smooth gas in position and momentum with a contact attraction acting only within a Gaussian gate, whose linear stability is bracketed between a broad-gate and a narrow-gate limit. See The gated Vlasov model.
General relativity; graviton. Einstein’s theory of gravity, in which the spacetime metric fixes distances and durations and its curvature is gravity. Small ripples of the metric are the graviton, a massless spin-2 field whose gauge symmetry is the linearized form of a change of coordinates. The program keeps general relativity as the long-range gravity of ordinary matter and uses the graviton as the template for X. See General relativity and the graviton.
Generalized metric (H). The positive metric on phase space, a ruler that measures position and momentum directions together. With the symplectic form it is one of the two fundamental structures under P2′, and the space of its compatible values is the Siegel domain. See The structures ω, η, H and the split-quaternion algebra and P1: the phase-space arena.
Geometric action S_H; v0.1 action. The complete action of the lab notebook’s version 0.1: five terms, with an Einstein-like term S_H for the phase-space metric written with ω and η frozen. It is superseded by P2′ and the Debt-1 calc notes; the name S_H survives as the action from which open problem 1 asks for the ghost-free potential to be derived. See The geometric action S_H and the v0.1 action (superseded).
Ghost. A mode whose kinetic term has the wrong sign, so that it carries negative energy or negative norm; once it interacts with ordinary matter the vacuum can decay, so a theory with an interacting ghost is not considered physical. Tachyons, gradient instabilities and strong coupling are different instabilities. See Ghosts and perturbative instabilities and The Fierz–Pauli mass term and the Boulware–Deser ghost.
“go”. Paul’s word for continuing with the next chunk of work. See The collaboration.
Goldstone angle. The toy models’ finding that the vacuum’s polarization is an angle that can turn at no cost in energy rather than a switch with two settings: where ρ sits inside a continuous U(1), the position-sharp and momentum-sharp vacua lie on one family, so a definite polarization needs an added potential. See The polarization as a Goldstone angle.
Goldstone mode; pseudo-Goldstone mode; Higgs mechanism. A Goldstone mode is the massless excitation that appears when the ground state breaks a continuous symmetry; a small explicit term that tilts the family of ground states gives it a small mass, making it a pseudo-Goldstone mode. When the broken symmetry is a gauge symmetry, the gauge field absorbs the would-be Goldstone modes and becomes massive: the Higgs mechanism. See Goldstone modes and the Higgs mechanism, and for a pseudo-Goldstone field that is an angle, Axion-like fields and pseudo-Goldstone bosons.
Graveyard. The register of the program’s dead claims, each linked to its obituary. See The graveyard: dead claims.
Gravitational Higgs mechanism. How X acquires its mass: the vacuum’s choice of polarization breaks the dual diffeomorphisms spontaneously, and X absorbs their would-be Goldstone modes and becomes a massive spin-2 field with five polarizations. See The gravitational Higgs mechanism.
Gravothermal self-limit. In calc note #4, the case in which heating and expansion throttle the condensation rate of Scenario A down to about one condensation per age of the system; even then an order-one fraction of an ultra-faint dwarf’s core is processed and removed. Gravothermal evolution is the slow redistribution of heat in a self-gravitating halo. See Obituary: Scenario A and the ultra-faint-dwarf endpoint and Self-interacting dark matter.
Grosse–Wulkenhaar (GW) model; model II. A renormalizable noncommutative scalar field theory that the Langmann–Szabo duality maps to itself at the parameter value Ω = 1; the program’s second toy model. The duality is a genuine symmetry for complex fields and only a covariance for real ones. See Model II: the self-dual Grosse–Wulkenhaar model.

H#

H-theorem. Boltzmann’s theorem that collisions drive a gas toward the smooth thermal distribution; Debt 3 used it to close the collisional route to velocity clumping. See Vlasov stability and Landau damping.
Handoff. HANDOFF.md, the note prepared on 2026-10-19 to carry the program from the claude.ai conversation to Claude Code and this repository: the scientific state on one screen, the artifact numbers #1–#15, the chat-only results, the method and a ranked queue. Its list of dead claims stays binding; its soliton candidate and its queue are superseded. See The handoff document.
Hard core. The assumption the program keeps fixed while it tests the rest: Born reciprocity is an exact symmetry of the laws that the vacuum breaks spontaneously, with only the symplectic form ω rigid and the neutral metric η as the order parameter. #11 records it as intact after two forced corrections. See The hard core: spontaneously broken Born reciprocity.
Hessian. The matrix of second derivatives of a potential at a stationary point, the mass-squared matrix of small oscillations: its zero directions are the flat directions, and a negative eigenvalue marks a saddle. The reduced-model stability rule requires it with all fields dynamical. See Goldstone modes and the Higgs mechanism and The reduced-model stability rule.
Hidden sector. A collection of particles and forces that takes no part in the strong, weak or electromagnetic interactions of ordinary matter; if nothing lets it exchange energy with our plasma, it keeps a temperature of its own, in a ratio ξ to ours. In #14, a hidden copy of a simple gauge force, SU(2)_d, broken to U(1)_d by an adjoint Higgs field, leaving heavy charged W′± bosons, a massless hidden photon, stable ’t Hooft–Polyakov monopoles and a light Dirac doublet ψ. As the program’s own proposal it is dead; as a model it is a standard scenario of the literature. See A hidden sector at its own temperature and Obituary: the hidden SU(2) → U(1) proposal.
Hidden sector’s thermal history. The record of how the soliton candidate’s hidden sector would have evolved as the universe cooled: the dark radiation of its hidden photon; the requirement that it start colder than ours by a temperature ratio ξ below 0.77, corrected in round 3 to 0.760, which #14 then applied inconsistently; and the gravitational-wave band a hidden transition would leave. See The hidden sector’s thermal history and, for the physics, A hidden sector at its own temperature.
Higgs portal. A coupling between the hidden adjoint scalar and our Higgs field, allowed by every symmetry #14 states; one of the constraints the round-3 referee found the manuscript had omitted. See Round-3 verdict, rulings and citation audit.
Higuchi bound. The condition m² ≥ 2H² for a massive spin-2 field on de Sitter space with Hubble rate H, below which the field carries a ghost; a heavy field meets it trivially. See Bimetric cosmology and its instabilities and the Higuchi ghost.
Hilltop quintessence. A scalar dark-energy field that starts near the top of a periodic potential and thaws away from w = −1; the program’s τ, with V = V₀[1 + cos(τ/f)]. See τ: hilltop quintessence on the Maslov circle and hilltop models.
Hypothesis H. #14’s coupling hypothesis, that the smallest hidden charge equals the electron’s; motivated but not derived, it fell with the candidate. See Obituary: the coupling α_d ≈ 34.

I#

Inflation; reheating. Inflation is a proposed early period of rapid, accelerating expansion that thins any relics produced before it; reheating is its end, when its energy turns into hot particles and sets the starting temperature of the radiation era. Inflation is the standard reason no monopoles of our own sector are seen. See Inflation, reheating and entropy dilution and The monopole problem.
Instability criterion. Debt 3’s threshold for a gas of gated dark matter to break up into velocity streams; see Mean-field criterion, below.
Invariant-length shell; Planck closure. #13’s Born image of the mass shell, x_μx^μ = λ_χ², which gives conjugate quanta an irreducible size, as ordinary quanta have a mass. A length times the maximum force is an energy, and at the Planck length it equals the Planck energy, which #13 calls “closure at the self-dual point”. See The invariant-length shell and Planck closure.
Inverse-Higgs constraints. Relations that turn some Goldstone-type fields of a broken spacetime symmetry into derivatives of others. Calc note #5 expects them to remove most of the nine extra moduli of Λ(d); this is open. See Inverse-Higgs constraints and Open: field content of the broken vacuum.
Iron rule. No arithmetic by eyeball: every number a document asserts or a reviewer disputes is computed by code that runs and prints its result, kept in verify/. See The iron rule: no arithmetic by eyeball.
Island. Collision. The particle island and the wave island are the two mass regimes of Debt 3: classical-particle χ, and χ light enough to be a classical wave. The “consistency islands” of #7 and #11 §15 are something else, the unique known consistent structures onto which the structural tests forced the program. See The classicality theorem and the particle island, The wave island and Assessment.
Island discriminant. Row 3: the tail of the self-interaction knee tells the islands apart, a sharp cutoff for particle χ and a (v*/σ)⁴ power law for wave χ. Its particle side assumes a sharp tail, whose shape is open. See Row 3: the island discriminant.

J#

Jeans instability. The gravitational instability in which a ripple in a gas longer than a critical length grows into a lump. The lab notebook described velocity clumping as the Jeans problem with the roles of position and velocity exchanged. See Vlasov stability and Landau damping and Obituary: velocity clumping, the founding image.

K#

Kalb–Ramond B-field. An antisymmetric tensor field, B_μν = −B_νμ, the 2-form gauge field of closed string theory, which does for a string what the electromagnetic potential does for a charged particle. Double field theory pairs it with the metric in its generalized metric. Holding ω rigid as well as η removes it (corollary 2 of the compatibility theorem), and it is the antisymmetric counterpart of the program’s symmetric momentum graviton X. See The Kalb–Ramond B-field.
Kibble mechanism; Kibble–Zurek. Topological defects form when the early universe cools through a symmetry-breaking transition, at least about one per horizon volume, because regions that have had no contact settle into unrelated vacuum states. Slow transitions (Kibble–Zurek dynamics) and first-order ones, which proceed by bubbles, make more, so the count is a floor, not a ceiling. See The Kibble mechanism.
Kibble normalization. The number p in the monopole yield n/s = p(T_c/M_Pl)³. #14 v3’s value had dropped the numerical prefactor of the expansion rate; corrected, one monopole per Hubble volume gives p ≈ 104, and the soliton candidate was retired. See Obituary: the Kibble normalization and the Kibble yield.
Kill condition. An observation, stated in advance, that would refute a claim. #11 §13 pairs each prediction with the result that would kill it, or marks the row as a diagnostic. See Predictions and kill conditions.
Kinetic mixing. A coupling between the field strengths of two U(1) forces, such as our photon and a hidden photon, of strength ε; when ε is not zero, hidden particles acquire a small electric charge under ours. Under strict P4 there is none beyond what gravity induces, ε ≲ 10⁻¹³, and none at all if hidden charge conjugation is exact. See Kinetic mixing between sectors.
Knee. The bend of the self-interaction cross-section σ_T(v) near the gate velocity v* ~ 10² km/s: strong scattering in slow dwarf galaxies, none in fast clusters. It replaced the cliff and is row 1. See Row 1: the knee in σ_T(v).
Knob. The documents’ word for a free parameter of an optional prediction. Row 10’s imprints are “knob-bounded”: a null result bounds the knobs rather than killing the program. See Row 10: an early step in G_eff.
Knot; π₂ monopole-class. Names used in HANDOFF.md and the popular articles for the retired superheavy dark-matter candidate. See Obituary: superheavy conjugate solitons and the two meanings of “soliton”.

L#

Lab notebook. Document #1, notes/broken-born-theory.md: the program’s first formal write-up, version 0.1 of September 2026, with five postulates, an action, a predictions table and a ranked list of open problems, followed by addenda v0.2–v0.6 that record each correction. Its body was never revised, so claims that later died still read there as live; it is superseded as reference. See The lab notebook (#1) and its addenda.
Lagrangian Grassmannian; Λ(d). The compact space Λ(d), equal to U(d)/O(d), of all ways of splitting a 2d-dimensional phase space into a position half and a momentum half. It has ten independent directions (moduli) at d = 4, its fundamental group is ℤ, generated by the Maslov circle, and it forms the Shilov boundary of the Siegel domain; in the program it is the space of possible vacuum polarizations. See The Lagrangian Grassmannian Λ(d).
Lagrangian polarization. A Lagrangian subspace is a set of phase-space directions, half the dimension of phase space, on which the symplectic form vanishes; choosing one, a polarization, is choosing which coordinates count as position. See Lagrangian subspaces and polarizations.
Lakatosian research program; protective belt. Lakatos’s unit of scientific appraisal: a hard core kept fixed, a protective belt of auxiliary hypotheses revised when predictions fail, and a judgement of progressive or degenerating. The program calls itself one, not a theory. See Lakatos’s methodology of research programmes.
Landau damping. The decay of a collective oscillation in a collisionless medium, such as a plasma, even though no collisions act. Below the instability threshold, ripples in the gated Vlasov model die away. See Vlasov stability and Landau damping.
Langmann–Szabo duality. A duality of noncommutative field theory that exchanges a field’s position and momentum descriptions, a Fourier transform of the field; the Grosse–Wulkenhaar model is mapped to itself by it at Ω = 1. See Noncommutative field theory and the Langmann–Szabo duality.
Lead. A result recorded but not established, such as the real Grosse–Wulkenhaar model’s one-loop preference for the position-sharp vacuum. See Open: the real model’s one-loop preference (a lead).
Linear photon dispersion. A correction to the speed of light proportional to a photon’s energy, which some approaches to quantum gravity predict and which gamma-ray-burst observations with the Fermi Large Area Telescope exclude at the Planck scale. Row 9 holds it exactly zero, protected by the half-turn ρ² in the lab notebook’s schematic argument. See Row 9: no linear photon dispersion.
Literature battery. The planned check of every reference cited from model memory (†) against its source, required before any external use; open problem 10 (OP10). Unrelated to the verification battery. See Open: the † literature battery (OP10).
Lyman-α forest. Absorption lines of intergalactic hydrogen in the light of distant quasars, which trace small-scale structure; its limits exclude wave dark matter that is too light. See Bounds on fuzzy dark matter.

M#

Machine-checked. Recomputed by a script in verify/ that runs in the gate, and tagged [V] where a document cites the result. A machine check confirms the arithmetic of the model the script encodes, not that the model is the right physics. See Verification.
Magnetic identification. A claim made only in the popular article #12: that the momentum-polarized sector is the magnetic side of electromagnetism, dark because its coupling is strong. No paper or note makes it, and it conflicts with dead claims, strict P4 and row 7, so the wiki records it as dead. See Obituary: the magnetic identification (popsci-only).
Magnetic mirror-family. The idea that every electrically charged particle, quarks included, has a magnetic counterpart: founding supposition 11, absorbed as established physics through Montonen–Olive duality, Seiberg’s magnetic quarks and the dual superconductor. See The magnetic mirror-family.
Magnetic monopole. A particle with magnetic charge alone, a north pole without a south pole. Gauge theories with a suitable symmetry breaking contain monopoles as stable, heavy field configurations, and none has ever been detected. See Magnetic monopoles.
Magnetic quarks. Standard vocabulary for the magnetic counterparts of quarks in Seiberg duality. See S-duality and Montonen–Olive.
Mandatory breaking. Because the canonical commutator rules out sharpness in both position and momentum, any world with local physics must select a polarization; in #11 §3’s words, “The magnet must point.” The argument requires some polarization but not which one. See Mandatory breaking: the uncertainty argument.
Maslov circle; Maslov phase. The loop in the Lagrangian Grassmannian that cannot be shrunk to a point, and the angle around it. The dark-energy field τ is this angle for the vacuum’s polarization, so it is periodic for topological reasons; that it is the only light modulus is postulated. See τ as the Maslov phase of the boundary.
Mass drain. In calc note #4, a condensate cycling through bosenovas throws an ultra-faint dwarf’s dark matter out as waves faster than the galaxy’s escape velocity, so the dark matter leaves the galaxy. See Obituary: Scenario A and the ultra-faint-dwarf endpoint.
Mass shell. The relation p_μp^μ = m²c² that every observer finds for a particle of mass m; #13’s invariant-length shell is its Born image. See The invariant-length shell and Planck closure.
Matrix base; duality lemma. The basis f_mn of the Moyal plane, built from harmonic-oscillator states, in which the star product becomes matrix multiplication and the Grosse–Wulkenhaar model becomes a matrix model. On it the Langmann–Szabo duality is left multiplication by parity, D f_mn = (−1)^m f_mn, a lemma credited to the work it follows from. See Model II: the matrix base and the action and The duality on the matrix base.
Maximum force. #13’s limit on how fast momentum can change, c̃ = ℏc/λ², the slope of the momentum-space light cone. With the Born length set to the Planck length it is c⁴/G, about 1.2 × 10⁴⁴ newtons, four times the literature’s conjectured c⁴/4G, a factor #13 leaves open. See The maximum force c̃ = c⁴/G.
Maximum-force conjecture; maximal acceleration. Proposals in the literature: that no force exceeds c⁴/4G (Gibbons’s maximum tension principle, and Schiller’s principle of maximum force), and Caianiello’s maximal acceleration from a metric on phase space. Both are proposals, and the first is contested. See Maximum force and maximal acceleration in the literature.
Mean-field criterion. The threshold for a gas of dark-matter particles with the gated attraction to break up into velocity streams, written g·n_gate ≥ m·min(σ, v*)² in #11: the attraction among particles that share a velocity must match the kinetic energy of their random motion. At the scattering benchmark it fails by 10²⁸–10³¹. See The mean-field criterion and its 10²⁸–10³¹ shortfall.
Measured failure mode. The record of where blind reviews have gone wrong. In rounds 1 and 2 the referees, without code, were reliable on structure and literature and unreliable on arithmetic; in rounds 3 and 4 the failures were on the author’s side, a wrong model input and a check run on a reduced model. See The measured referee failure mode.
Merger band. Comparable-mass black-hole mergers, which reach forces of the order of the maximum force: the one natural arena #13 names where dual-kinematic corrections could be of order one. No signature has been derived. See Force boosts and force composition.
Mermin–Wagner–Coleman theorem. In two dimensions a compact continuous symmetry cannot break spontaneously; discrete and some non-compact symmetries escape it. It is why the toy models’ polarization angle can order only after a potential reduces its symmetry to a discrete one. See The Mermin–Wagner–Coleman theorem.
Millicharged particle. A particle with a tiny electric charge, such as the hidden fermion ψ would acquire through kinetic mixing; strict P4 closes the case. See Kinetic mixing between sectors.
Mirror vacuum. The vacuum polarized the other way, organized around momentum, which satisfies the same laws as ours. See P5: the vacuum selects a polarization.
Misalignment. Collision. The misalignment mechanism produces a light field displaced from its potential minimum in the early universe, which later oscillates as cold dark matter; it gives wave-island χ its relic abundance. The misalignment potential is the energy cost of a mismatch between the polarization J and the modular field Z; it gives X its mass. See The misalignment mechanism, Relic abundance by misalignment on the wave island and The misalignment potential.
Model I; model II. The two toy models: the coset sigma model of a phase-space metric H and a real structure K, and the self-dual Grosse–Wulkenhaar model. Model I’s action is unchanged by ρ, while each of its vacua is carried by ρ to a different one; with a bounded potential it meets acceptance criterion 1 in the referees’ wording. In model II the complex version’s breaking does not survive quantization. See Model I: the coset sigma model, Model I: action and symmetries, Model I vacua and Model II: the self-dual Grosse–Wulkenhaar model.
Modular field. The single complex symmetric matrix field Z = X + iY, with values in the Siegel domain, that carries all of phase-space geometry once only ω is rigid: Im Z = g is the spacetime metric and Re Z = X the momentum graviton. See The modular field Z = X + iY.
Modular group SL(2, ℤ). The group of 2 × 2 matrices with whole-number entries and determinant 1, generated by S: z → −1/z and T: z → z + 1, which acts on the upper half-plane. It carries a lattice of electric and magnetic charges onto itself and acts on the complexified coupling τ_c; S as an exact symmetry of a quantum theory is S-duality. The matrix of S is also that of Born reciprocity and of Z → −Z⁻¹, where it belongs to a continuous group. See The modular group SL(2, ℤ).
Modular inversion; Möbius action. Born reciprocity acting on the modular field as the fractional-linear map Z → −Z⁻¹, whose fixed point Z = i is the self-dual vacuum; on the vacuum slice it sends the metric to its inverse. See Reciprocity as modular inversion Z → −Z⁻¹.
Momentum clumping. Dark matter clumping in velocity rather than in space, the founding image; tested in Debt 3 and dead as dynamics. See Momentum clumping (Debt 3) and Obituary: velocity clumping, the founding image.
Momentum fiber. The space of momenta attached to one point of space-time. General relativity leaves these fibers flat, which Born’s question counts as an assumption, and the gate mechanism acts through the overlap of wavepackets along them. See Momentum fibers and the cotangent bundle and The gate mechanism.
Momentum graviton (X). X = Re Z, the symmetric tensor field that carries the geometry of momentum space and changes sign under reciprocity: its symmetries make it a second graviton, consistency makes it massive, and ordinary matter feels it at gravitational strength but only over a short range. #12 calls it “the second geometry”; #6 calls it the “symplectic partner of the graviton”. See The momentum graviton X.
Momentum-space black holes; velocity traps. A chat-only conjecture: a black hole’s horizon read in the momentum description as the surface where hovering requires the maximum force, with mirror objects trapped in momentum rather than in space (“velocity traps”) and “dual Hawking quanta” huge in position space. No document derives it. See Momentum-space black holes (chat-only).
Monopole problem. The hot early universe should have produced superheavy magnetic monopoles in unacceptably large numbers, and annihilation removes too few; the standard remedy is inflation. See The monopole problem.
Monte Carlo (MC). Simulation by random sampling. The toy-model note’s Monte Carlo of the frozen-H lattice model reports error bars from four independent seeds; a Monte Carlo with H dynamical is open. See Monte Carlo: an ordered ℤ₂ phase and Open: a Monte Carlo with H dynamical.
Monte Carlo error-bar rule. Numbers from a random simulation need error bars from independent runs: a fixed seed makes a number reproducible, not accurate. It was round 4’s second lesson. See The Monte Carlo error-bar rule.
Montonen–Olive duality. The proposed exact electric–magnetic duality that exchanges electrically charged particles with monopoles, and strong with weak coupling; exact in maximally supersymmetric Yang–Mills theory. See S-duality and Montonen–Olive.
Moyal plane; star product. The noncommutative plane, [x₁, x₂] = iθ, which behaves like the phase space of a quantum particle, and the product of functions that builds that relation in; the setting of the Grosse–Wulkenhaar model. See Noncommutative field theory and the Langmann–Szabo duality.
Multi-graviton no-go theorem. Boulanger, Damour, Gualtieri and Henneaux’s theorem that several massless spin-2 fields cannot interact with one another consistently; it excludes a massless X. See The multi-graviton no-go theorem.
Mutual locality. Two charges are mutually local when their DSZ pairing vanishes, so that they can share one Lagrangian description. See The symplectic charge lattice.

N#

Naive ρ-preserving potential. The first potential added to model I to pin its polarization, −μ[Tr(K K_ref)]². Once the metric H varies it is unbounded below and its intended vacuum is a saddle (round-4 findings F1 and F2); it is dead and kept as the counterexample that the bounded potential answers. See Obituary: the naive ρ-preserving potential.
Net theorem. Debt 3’s summary result, that velocity clumping is nowhere a required consequence of the program: in #9’s words, “forbidden (particles), fatal (wave, committed coupling), decorative (wave, free coupling)”. Clumping is impossible for particle dark matter, ruled out by observation where a fixed coupling would make it mandatory for waves, and merely optional where the coupling is free. See The net theorem: clumping is nowhere mandatory.
Neutral metric (η). A symmetric pairing on phase space with as many positive as negative directions, whose null directions mark out which coordinates count as position and which as momentum. Under P2′ it is not fixed but chosen by the vacuum, as the order parameter of the broken symmetry, and ρ reverses its sign. See The structures ω, η, H and the split-quaternion algebra.
Noncommutative field theory. Field theory on a space whose coordinates do not commute, such as the Moyal plane. See Noncommutative field theory and the Langmann–Szabo duality.
Nontriviality theorem. The program says anything beyond general relativity plus one model of self-interacting dark matter only if the neutral metric η is a property of the vacuum rather than fixed background; it forced the change from P2 to P2′. See The nontriviality theorem.
No-phantom bound. The requirement that the dark-energy equation of state never fall below −1, because τ is an ordinary scalar field obeying the null energy condition; a robust intrinsic w < −1 would kill the framework outright. See The no-phantom bound w ≥ −1.
“No timescale refuge”. Calc note #4’s finding that condensation in an ultra-faint dwarf takes so small a fraction of the galaxy’s lifetime that slowing it does not save Scenario A. See Wave kinetics and Bose-star formation and Obituary: Scenario A and the ultra-faint-dwarf endpoint.
Null energy condition. A standard requirement on reasonable matter, which an ordinary scalar field obeys and which keeps its equation of state at w ≥ −1; a phantom phase requires violating it. See The phantom divide and the null energy condition.

O#

Obituary. A page on a dead claim: what was claimed, how it was tested, why it failed and what survives. #11 §9 and §12 are written as obituaries. See The graveyard: dead claims.
Occupation number. The average number of quanta sharing one quantum state, or mode, N_occ. When it is much greater than one the dark matter behaves as a classical wave and its scattering rates are Bose-enhanced. See Occupation number: particles or waves.
Omitted constraints. The bounds the round-3 referee found #14 had not evaluated, among them re-thermalization through a millicharge, supernova and nucleosynthesis limits, dark acoustic oscillations, the Higgs portal and reheating; the adjudication accepted the list as a to-do. See Round-3 verdict, rulings and citation audit.
One loop. The first quantum correction to a classical result. In the real Grosse–Wulkenhaar model it separates two vacua of equal classical action and favours the position-sharp one, a lead. See Open: the real model’s one-loop preference (a lead).
OP1–OP11 (OPn). Item n of the eleven open problems of #11 §14; OP1–OP3, deriving the wedge sector from S_H, the partially-massless comparison and the Lorentzian dressing, are the items on which #11 makes the word “theory” wait. Open pages give the number in their titles. See Open problems and the queue.
Orbital stirring. The mixing of a halo’s velocities by its own orbits, at a rate Ω = 1/t_dyn, against which Debt 3 compared the growth of streams; below the instability threshold there is no growth to compare, which retired the earlier “γ vs Ω” framing. See The gated condensation rate Γ_self and The gated Vlasov model.
Order of precedence; source conflicts. The fixed ranking that decides which document the wiki follows when two disagree, from the root CLAUDE.md section “Since the handoff” first to the popular articles last; disagreements it does not settle are stated as unresolved. See Documents and Conflicts between sources.
Order parameter. The quantity that is zero while a symmetry is intact and takes a definite value, which the symmetry would change, once it is broken, as a magnet’s magnetization does. For reciprocity it is the neutral metric η, written through J or K in different documents, which do not agree on which to call “the real structure”. See The order parameter: J, η and K.
Ordered ℤ₂ phase. The phase the frozen-H Monte Carlo finds with the potential switched on: one of two vacua, exchanged by ρ, is singled out on every lattice size. ℤ₂ is the two-element symmetry group. Version 2 of the toy-model note uses the term in place of the earlier “Ising class”, since data at one temperature establish order but not a universality class. See Monte Carlo: an ordered ℤ₂ phase and The frozen-H reduction.
Over-constraint. Once its height is fixed by the measured amount of dark energy, the dark-energy model has two free parameters (f, τᵢ) but must fit three observables (w₀, wₐ, t_turn), which gives one built-in test; the third observable lies in the far future. See The dark-energy over-constraint.
Overproduction. The corrected result that retired the soliton candidate: with one monopole per Hubble volume, the monopoles match the dark-matter density only at a mass of 2.9–4.4×10¹² GeV, and #14 v3’s benchmark of 3×10¹³ GeV is overproduced 2.1×10³ to 1.2×10⁴ times. See Overproduction at the benchmark.

P#

P1–P5; P2; P2′. The five postulates. P1: physics lives on phase space with a symplectic form ω and a generalized metric H. P2′: only ω, the constancy of ℏ, is fixed; it replaced the original P2, which also froze η and left the program with no content of its own. P3: the action is invariant under Born reciprocity. P4: ordinary matter is position-polarized and conjugate matter momentum-polarized, with only gravity acting between them. P5: the vacuum selects a polarization. See Postulates P1–P5, P1, P2′, Original P2 (superseded), P3, P4 and P5.
P4 lock. In the coset toy model, nothing requires matter to couple to the sign of the order parameter; postulate P4, which places ordinary matter in the position-polarized representation and its mirror in the momentum-polarized one, supplies the link. So the toy explains locality in position only as part of a package with a momentum-local mirror sector. See Open: forced locality and the P4 lock.
Palindrome; palindromic branch; interchange-symmetric branch. The constraint βₙ = β₄₋ₙ that reciprocity, acting as the exchange of the potential’s two frames, imposes on the five coefficients of the bimetric potential, so that the list reads the same forwards and backwards; and the family of potentials that satisfy it. See The palindrome βₙ = β₄₋ₙ and The palindromic branch.
Para-Hermitian geometry. Geometry with a real structure whose two eigenspaces are null for a compatible neutral metric; calc note #5 §F names it as the literature nearest to Born geometry. See The structures ω, η, H and the split-quaternion algebra.
Parker bound; MACRO. The upper limit on the flux of magnetic monopoles set by the survival of the Galaxy’s magnetic field; the extended Parker bound applies the same argument to the young Galaxy’s seed field. Direct searches, among them the Monopole, Astrophysics and Cosmic Ray Observatory (MACRO), have found none. See Monopole flux bounds: Parker and MACRO.
Partially massless (PM) gravity. A spin-2 field on de Sitter space at the one mass where an extra gauge symmetry removes one of its polarizations; and the bimetric parameter point studied as partially massless bimetric gravity, which lies inside the palindromic branch at α = 1. Whether reciprocity is the origin of its symmetry is part of open problem 2 (OP2). See Partially massless gravity and Open: the partially-massless comparison (OP2).
Particle island. Classical-particle χ, with masses from MeV to GeV, on which the self-interaction knee survives but collective momentum-space behaviour is impossible. See The classicality theorem and the particle island.
Patch modes; co-movers. In calc note #2’s narrow-gate limit, perturbations confined to a small ball of momentum space, and the particles inside it, which move within the gate width of one another. See The mean-field criterion.
Permanent null. A prediction that a search will never find anything: rows 7–9, no non-gravitational dark-matter signal, no monopole of our sector and no linear photon dispersion. See Predictions and kill conditions.
Phantom crossing; phantom divide. w = −1 divides ordinary dark energy from phantom dark energy, which becomes denser as space expands; an ordinary scalar field cannot cross it. Data Release 2 of the Dark Energy Spectroscopic Instrument favours a crossing to w < −1 above redshift z ≈ 0.4, against the program’s requirement. See The phantom divide and the null energy condition and DESI DR2’s phantom crossing.
Phase. Collision. Phase space is the space of positions and momenta; a phase of matter, such as the ordered ℤ₂ phase, is a thermodynamic state; the Maslov phase and the condensate phase β of model II are angles; and a phantom phase is a period with w < −1. See the entries for each.
Phase space. The space of positions and momenta taken together, the program’s arena (P1). See Phase-space geometry.
Phase-space diameter relation. A chat-only conjecture, D_x·D_p = h·N^{1/3} per dimension: the universe’s diameters in position and in momentum multiply to Planck’s constant times a large number, a cosmological counterpart of the time–bandwidth product. A note on it is queued. See The phase-space diameter relation (chat-only).
Planck units; Planck mass; reduced Planck mass. The length, energy and mass that can be formed from ℏ, c and G: the Planck length l_P = √(ℏG/c³), the Planck energy and the Planck mass. Their energy-to-length ratio, c⁴/G, is also called the Planck force. The Planck mass also sets how strongly a spin-2 field couples to matter, and it is written in two conventions, M_Pl = G^{−1/2} and the reduced M̄_Pl = M_Pl/√(8π), one of which a formula keeps throughout. See Planck units and the two Planck masses.
Polarization. Collision. In the program, a choice of Lagrangian subspace, that is, of which variables count as position: ordinary matter is x-polarized, conjugate matter p-polarized, and our vacuum x-tilted. In model II the polarization Δ(β) measures how much broader a vacuum is in position than in momentum. The word keeps its ordinary meanings elsewhere, as in the five polarizations of a massive spin-2 field. See Lagrangian subspaces and polarizations, P4: polarized matter and strict sector separation, P5: the vacuum selects a polarization and Complex-model vacua and the polarization Δ(β).
Polarization-genesis. The program’s name for a mechanism it does not yet have, which would set the ratio Ω_χ : Ω_b = 5.4 : 1 of dark to ordinary matter as baryogenesis sets the baryon excess; the lab notebook’s sketch is “a shape, not a mechanism”. It is open problem 7 (OP7). See Open: polarization-genesis and the 5.4 : 1 ratio (OP7).
Popsci-only. Said of a claim found only in the popular articles #10 and #12, of which #12 presents the framework as if it were confirmed; never a source for a claim’s status. See Conjectures: chat-only and popsci-only claims.
Popular articles. “The Angle of the Mirror” (#10), a narrative of the program’s first week, and “The Universe’s Other Half” (#12), a tour of the framework written “as if it were confirmed”. Both are kept for their exposition and rank last among the sources. See The popular articles (#10, #12).
P.R. Paul, an independent developer, who supplies the program’s conjectures and direction and holds a veto; Claude supplies derivations, counterexamples, verification and drafting. See The collaboration: roles, attribution and conventions.
Pre-registration; weakest link. Writing down and committing, before each review round, the expected verdict and the weakest point the referee is expected to find, then scoring the forecast. Since round 3, whose forecast leaked through a commit subject that the referee could see, forecasts are kept out of commit subjects. See Pre-registration and its calibration record and Round-3 pre-registration.
Predictions not previously posed. #11 §15’s progressive sign for predictions that no earlier work had made: rows 3 and 11. See Assessment.
Predictions table. #11 §13’s list of eleven observables, each with what standard physics expects, what the program requires and the result that would kill it. See Predictions and kill conditions and History of the predictions table.
Program-native. Depending on Born reciprocity for its content. The soliton candidate was retired as a program-native proposal; its surviving low-mass version is prior art to which the framework adds nothing testable. See Obituary: superheavy conjugate solitons.
Progressive; degenerating. Lakatos’s appraisal of a research program: progressive while its revisions lead to new predictions, some of them confirmed; degenerating while they only absorb failures. #11 §15 lists the program’s signs of each. See Lakatos’s methodology of research programmes and Assessment.
Project instructions; “Since the handoff”. The root CLAUDE.md, the repository’s standing instructions: the program statement, the layout, the gate, the method and the working arrangement with Paul. Its section “Since the handoff” is the most current statement of the program’s status and ranks first among the sources. See CLAUDE.md and the README.
Provenance tags. See [D], [T], [P], [O], [V] under Numbers and marks.
ψ relic window (psi). The range of masses #14 v3 allowed for ψ, the light hidden fermion added so that the W′± bosons could decay. Round 3 found both edges wrong: the upper edge left out the antiparticle and the second member of the doublet, and at the lower edge ψ would still be freezing out during nucleosynthesis. The window is dead. See Obituary: the ψ relic window.

Q#

Quantum restoration. In the complex Grosse–Wulkenhaar model every condensate phase is an exact flat direction and the condensate is a localized lump with no volume factor, so quantum fluctuations restore the symmetry the classical vacua break: criterion S4 fails for that route. See Quantum restoration in the complex model.
Quarantined. Kept on record but set apart from the program’s commitments: Scenario B, alive but listed among the degeneration risks, and the chat-only and popsci-only claims, which the conjectures register keeps apart from the derived record. See Scenario B: tunable streams (quarantined) and Conjectures: chat-only and popsci-only claims.
Queue. The ordered list of next tasks, kept in the root CLAUDE.md, which superseded the handoff’s ranked list. Its first item is the partially-massless comparison, the † literature battery and the phase-space-diameter note; a round-5 review of the toy-model note is optional. See Open problems and the queue.
Quintessence; thawing; freezing. Dark energy made of a slowly changing scalar field. In a thawing model the expansion holds the field nearly still at early times and it starts to change late, so w begins near −1 and rises; a freezing field moves early and slows toward −1. Row 4 requires w₀ > −1 and wₐ < 0, never phantom. See Quintessence and the equation of state, Thawing and freezing quintessence and Row 4: thawing dark energy, never phantom.

R#

Radiation era; yield. The early period in which radiation and fast particles dominated the universe’s energy, so that the temperature alone set the expansion rate. A relic’s yield, its number density divided by the entropy density, stays fixed once it is no longer made or destroyed. The soliton candidate’s central error was a dropped factor of the radiation-era expansion rate. See The radiation era: thermal history and N_eff and The relic yield Y = n/s and entropy dilution.
Real structure (K). An operator on phase space that squares to +1, leaving one line in place and reversing another; its two eigenlines are the candidate position and momentum axes. In the toy models K carries the order parameter, with η = ωK; #11 and the toy-model note disagree on which operator to call “the real structure”. See The order parameter: J, η and K and The structures ω, η, H.
Reciprocity parity; even and odd combinations. Reciprocity exchanges the program’s two spin-2 frames, so the fields of definite mass are their sum, unchanged by the exchange (reciprocity-even), which is the massless graviton, and their difference, which changes sign (reciprocity-odd), which is X. Row 6 rests on it. The assignment uses reciprocity as the exchange of the frames; under #11 §6’s Z → −Z⁻¹ the metric’s fluctuation changes sign too (flag 39 in review/wiki-build-flags.md). See Spectrum, parameters and reciprocity parity and Row 6: the exactly massless graviton.
Redshift. The stretching of every wavelength of light by the expansion between emission and observation, written z; the momentum of any freely moving particle falls in the same proportion: 1 + z = a₀/a_e. See Redshift.
Reduced-model stability rule. When numerics run on a model with some fields frozen, check the full model’s boundedness and Hessian with all fields dynamical, and say in the text that it is a reduction; round 4’s first lesson. See The reduced-model stability rule.
Relic abundance. The density a particle species retains from the hot early universe, and the mechanisms that set it. See Relic abundance mechanisms.
Review rounds 1–4. The four blind reviews: rounds 1 and 2 of #14 v1 and v2 (B, and “B near B/C”), round 3 of #14 v3 (C) and round 4 of the toy-model note (B). See Blind review, Review rounds 1 and 2, Review round 3 and Review round 4.
ρ-preserving potential (rho). A potential on the polarization angle, unchanged by ρ and by K → −K, that reduces the continuous symmetry to a discrete one and so makes the polarization definite. It brings in a fixed, unordered pair of axes, more structure than ω alone, and no derivation of it exists. See Open: the origin of the ρ-preserving potential and The bounded potential V_b.
Rindler frame. The frame of an observer under constant acceleration in flat space-time; in #13’s dual kinematics a constant force, uniform dual motion, is such a frame. See Rindler frames and Dual inertia: free fall as rest.
Rows. Collision. The rows of #11 §13’s predictions table. The lab notebook’s table and the Debt-3 notes number an older set, whose rows 3 and 4, velocity granularity and Fornax friction, are withdrawn. See Predictions and kill conditions, History of the predictions table, Obituary: velocity-space granularity in halos and Obituary: Fornax friction suppression.
Rulings (round 3); upheld, accepted, overturned. The adjudicator’s decisions on the round-3 referee’s thirteen numbered findings: most upheld, others accepted, some of them without re-checking, and one overturned, the claim that a cited paper lacked the operator it was cited for. See Round-3 verdict, rulings and citation audit.

S#

S0–S5. The six pass-or-fail criteria fixed, with forecasts, before the toy models were built: S0–S3, the referees’ letter (prior work cited, a symmetric action, vacua that the symmetry permutes, an order parameter), and S4–S5, the spirit (the breaking survives quantum fluctuations and makes matter local in position). See Success criteria S0–S5 and the pre-registered predictions.
S-duality. Electric–magnetic duality as an equivalence between a gauge theory at strong coupling and one at weak coupling, acting on the complexified coupling as τ_c → −1/τ_c through the same matrix [[0, 1], [−1, 0]] as ρ; established only in special supersymmetric theories. See S-duality and Montonen–Olive.
Scale factor. The number a(t) that multiplies the distances between distant galaxies and tracks the expansion; the conjugate universe has its own, ã. See Friedmann cosmology and minisuperspace.
Scale-factor duality. The program’s reciprocal relation a·ã = 1 between our scale factor and the conjugate one, which on the vacuum slice is the map g → g⁻¹; it makes the far-future halt of our expansion the conjugate universe’s bounce. See Scale-factor duality.
Scattering isotropy. Row 2: below the gate velocity, gated scattering through a heavy carrier goes equally in all directions, unlike the forward-peaked scattering of models with a light force carrier. It holds for particle χ only. See Row 2: isotropic scattering below the gate.
Scenario A; Scenario B. Calc note #3’s two wave-island scenarios. In A the gated channel makes dwarf-galaxy cores, which forces condensation in ultra-faint dwarfs and drains their dark matter; it is falsified. In B the cores come from elsewhere, and streams are tunable but never required; it is alive but quarantined. See Obituary: Scenario A and the ultra-faint-dwarf endpoint and Scenario B: tunable streams (quarantined).
Section condition; strong constraint. A rule from double field theory that makes every field depend on only half of a doubled set of coordinates. Built from η in the toy model, it confines matter to one of η’s two null lines but cannot say which one is position; the clean two-way choice holds only for one position and one momentum. See The section condition: what η fixes and Double field theory and the generalized metric.
Sector separation (strict P4). No gauge force acts between the two polarizations of matter, read strictly since #11 v2.1 (round-3 Decision 1): no kinetic mixing beyond what gravity itself induces. See P4: polarized matter and strict sector separation.
Segue 1. An ultra-faint dwarf galaxy, among the densest and most dark-matter-dominated systems known, whose stars about 13 billion years old sit in an intact halo; it falsified Scenario A. See Dwarf galaxies: cores and ultra-faint dwarfs.
Selection-versus-derivation bias. The risk #11 §2 names, which the wiki reads as presenting a structure chosen from the known consistent options as though the program’s premises had forced it; the ghost-free class of the tuning test, for one, was selected, not derived. See Claim tiers and selection bias.
Self-dual. Collision. The self-dual point Z = i is the fixed point of ρ on the modular field, and calc note #5 calls the circle |Z| = 1 the self-dual circle, identifying it with a·ã = 1 (queried as flag 23). The self-dual point of the Grosse–Wulkenhaar model is Ω = 1, where the Langmann–Szabo duality maps it to itself. #13’s “closure at the self-dual point” is the result that at the Planck length the invariant-length shell gives the Planck energy, and Born’s self-dual program sought a physics with a fundamental mass and a fundamental length. See Reciprocity as modular inversion Z → −Z⁻¹, Noncommutative field theory and the Langmann–Szabo duality and The invariant-length shell and Planck closure.
Self-interacting dark matter (SIDM). Dark matter whose particles scatter off one another through a force of their own; the scattering carries heat into a halo’s centre and turns a steep density peak into a flat core. Conjugate matter is a gated version. See Self-interacting dark matter.
Shift symmetry. Adding a constant matrix to X leaves every geometric action of the program unchanged, because the shift is one of the maps that preserve ω. So the geometry gives X no potential, and X either propagates or does not exist. See Shift symmetry: X is never auxiliary.
Shilov boundary. The distinguished part of the Siegel domain’s edge, which is the Lagrangian Grassmannian Λ(d); the dark-energy field lives on it. See The Lagrangian Grassmannian Λ(d).
Siegel domain; Siegel half-space; Siegel disk. The space Sp(2d, ℝ)/U(d) of complex symmetric matrices Z with positive-definite imaginary part, the matrix version of the upper half-plane; each point names one phase-space metric compatible with ω. HANDOFF.md §8 refers to its disk model. See The Siegel domain Sp(2d, ℝ)/U(d).
Sigma model; coset sigma model; hyperbolic sigma model. A field theory whose field takes values in a curved target space; in a coset model the target is a group divided by a subgroup. Non-compact hyperbolic models, unlike compact ones, can break symmetry in two dimensions, which leaves open whether model I’s coupled sectors break the SO(2) that contains ρ without a potential. See Coset and hyperbolic sigma models and Open: does ρ’s SO(2) break in the coupled model?.
Sign of V(τ). An unresolved conflict in the documents: the dark-energy potential as written, V₀[1 + cos(τ/f)], is never negative for V₀ > 0, yet the turnaround needs it to become negative (flag 27 in review/wiki-build-flags.md). See Open: the sign of V(τ) and the turnaround.
Signature obstruction. Without a gauge symmetry, no symmetric tensor field in spacetime’s signature has a ghost-free two-derivative kinetic term, which excludes an X without its gauge symmetry. See The signature obstruction and Why X must be massive.
Skeptic review console. Artifact #15, a single HTML page that sent #14 to a fresh referee with web search and an adversarial prompt in rounds 1 and 2; its prompt defines the A/B/C verdict scale. It is kept as the record of those rounds. See The skeptic review console.
Slaved momentum metric; slaved geometry. The momentum metric fixed as the inverse of the position metric, g̃ = g⁻¹, by the compatibility theorem; under P2′ it holds only on the vacuum slice, and #13’s dual cone belongs to it. See Corollaries: unimodularity, no B-field, slaved momentum metric.
Soccer-ball problem. The difficulty, for any theory with curved momentum space, of explaining why the curvature does not show up in the large total momenta of everyday bodies. The lab notebook lists it as its sixth open problem, with a standard rescaling as a patch that it calls ad hoc, and no later document returns to it. See Curved momentum space.
Soliton. Collision. In the Debt-3 notes (#3, #4), the Bose-star core of a wave-dark-matter halo. In #14 and #11 §12, a topological defect: a ’t Hooft–Polyakov monopole of the hidden sector. #11 §11.3 also calls magnetic states “solitonic”. See two meanings of “soliton”, Wave kinetics and Bose-star formation, The soliton candidate (retired) and Obituary: superheavy conjugate solitons.
Soliton candidate (retired); superheavy conjugate solitons. The proposal that dark matter consists of superheavy magnetic monopoles of a hidden gauge force, the third candidate of #11 v2.0 and the subject of the manuscript #14. Round 3 found its monopole count misnormalized; it was retired on 2026-10-19 and stays dead, and its low-mass version is published prior art. See The soliton candidate (retired) and Obituary: superheavy conjugate solitons.
Soliton-obituary script. verify/soliton_obituary.py, which recomputes, after four anchors independent of the manuscript, the numbers of the round-3 rulings behind the soliton candidate’s death. Flag 33 in review/wiki-build-flags.md notes that its checks cover less than its closing line says. See The soliton-obituary script.
Sommerfeld enhancement. The growth of an annihilation rate at low velocity caused by a long-range attraction; #14 left open whether it, with rapid bound-state formation, would change the monopoles’ abundance. See Obituary: the √N topological floor (chat-only).
Special relativity. Einstein’s 1905 theory of how measurements of length and time compare between observers moving at constant velocity, built on one speed that all of them measure alike; #13 copies its machinery into the momentum polarization, with force in place of velocity. See Special relativity: the template.
Spectrum. Collision. In the program’s central analogy, the spectrum of a waveform, which stands for a state’s momentum description; elsewhere, the spectrum of a theory is its list of particles and their masses, as in model I’s Goldstone spectrum or the spin-2 spectrum of bimetric gravity. See The Fourier transform as a phase-space rotation and Spectrum, parameters and reciprocity parity.
“Spent” coupling. Calc note #2’s word for a coupling already fixed by one fit, the dwarf-core cross-section, which leaves no freedom for another. See The scattering benchmark.
Spin-2 field. A symmetric tensor field whose quanta carry two units of angular momentum. The graviton is the massless case, and a mass or a second such field can be added only in narrow ways without a ghost. See Spin-2 fields.
Split-quaternion algebra. The algebra of the three operators built in pairs from ω, η and H: one squares to −1, the other two square to +1, and the product of the first two is the third. See The structures ω, η, H and the split-quaternion algebra.
Spontaneous symmetry breaking (SSB). A symmetric law with an asymmetric ground state, as a cooled magnet points one way although the laws governing its atoms treat all directions alike; the symmetry then relates the possible ground states to one another. The program proposes that Born reciprocity is broken in this way. See Spontaneous symmetry breaking and Spontaneous breaking of reciprocity.
Status words; folded items; registers. Each wiki page has one status: established (literature), alive (a program claim that stands), conjecture, open, dead, superseded (replaced by a corrected version), method, record or hub. A minor item of another status on a page has a heading of its own, such as “Open: …” or “Superseded: …”. The registers list the claims by status. See Status of the program’s claims, Claims that stand, The graveyard, Open problems and the queue, Conjectures and Superseded statements.
Strong form; weak form (of S5). Criterion S5 asks the vacuum’s polarization to make matter’s interactions local in one variable. The weak form, with matter’s coupling to the order parameter given, passes with a coupling built from H and K; the strong form, with that coupling required by the theory, is open. See Locality from an (H, K)-built coupling and Open: forced locality and the P4 lock.
Structural; rigorous. Qualifiers the calc notes attach to the tag [D]. No document defines them. In use, “[D — rigorous]” marks a complete derivation, and “[D — structural]” an argument that fixes the form or the class of a result without deriving it line by line, as when calc note #8 says the wedge-sector class “was selected by minimality + consistency, not derived line-by-line”. See The three debts and Provenance tags and citation marks.
Stückelberg fields. Fields that keep a massive gauge theory gauge-invariant, the would-be Goldstone modes written out as fields, as in A_μ + ∂_μπ for a massive vector; here, the modes that X absorbs, which #11 calls the Stückelberg sector. How strongly τ mixes with them is open problem 6 (OP6). See Stückelberg fields and Open: τ–Stückelberg mixing (OP6).
Symplectic form; symplectic group. The antisymmetric pairing ω of positions with momenta that underlies Hamiltonian mechanics and the quantum commutator, measuring signed area in each position–momentum plane. The group Sp(2d, ℝ) of linear maps that preserve it contains rotations such as ρ, boosts and squeezes. In the program ω is the one rigid structure, read as the constancy of ℏ. See The symplectic form and Sp(2d, ℝ).
Symplectic partner of the graviton. Calc note #6’s observation: doubling geometry with the symmetric η pairs the metric with a harmless antisymmetric B-field, whereas doubling with the antisymmetric ω pairs it with a second graviton. #11 offers it as the structural reason string theory’s doubling works while Born’s stalled. See The symplectic partner of the graviton is another graviton.
Symplectic vielbein. The frame E with H = EᵀE. Wedge polynomials of E and the polarization frame E₀[J] form the ghost-free frame tier. See The frame tier: the symplectic vielbein.

T#

’t Hooft–Polyakov monopole; Bogomolny–Prasad–Sommerfield (BPS) limit. A stable, particle-like field configuration of a gauge theory whose SU(2) symmetry is broken to U(1) by an adjoint Higgs field; it cannot decay because its Higgs field winds once around the sphere of vacua. Its mass is 4πf v/g_d, with f = 1 in the Bogomolny–Prasad–Sommerfield limit, rising to about 1.79 at larger self-coupling. The soliton candidate’s monopoles were of this kind. See The ’t Hooft–Polyakov monopole.
Tadpole. The coefficient T of the bimetric potential’s term that is linear in a small departure from the aligned point. See The vacuum-energy identity V(1) = 2T.
τ (tau). The program’s dark-energy field: the angle of the vacuum’s polarization around the Maslov circle, with a periodic potential, held near its maximum and slowly thawing. See τ: hilltop quintessence on the Maslov circle and τ as the Maslov phase of the boundary.
τ is not eaten. The result that τ is not among the modes X absorbs when it becomes massive, because constant shifts of X do not generate the compact directions in which τ lies; derived at leading order. See τ is not eaten.
Theory (the word). #11 holds back the word “theory” until open problems 1–3 are settled: deriving the wedge sector from S_H, the partially-massless comparison and the Lorentzian dressing. Until then the program describes itself as a research program. See Assessment.
Tier. Collision. Claim tiers 1–3 are #11’s trust strata. The metric and frame tiers are the second- and first-order formulations of the tuning test. The toy-model worklog groups its success criteria into tier 1 (the letter, S0–S3) and tier 2 (the spirit, S4–S5). The handoff’s “conjecture tier” labels chat-only conjectures, and #13 marks its dual second law “conjecture-tier”; neither is a house tag. See Claim tiers and selection bias, The frame tier and Success criteria S0–S5.
Time–bandwidth product. The signal-analysis rule that a pulse cannot be both very short in time and very narrow in frequency; the uncertainty principle is the same trade-off applied to the wavefunction, and the phase-space diameter relation is offered as its cosmological counterpart. See The Fourier transform as a phase-space rotation.
Topological dark matter; prior art. Dark matter made of topologically stable defects of a hidden sector, such as monopoles. The published PeV-scale scenario is what remains of the soliton candidate once its abundance is counted correctly, and the program claims only compatibility with it, as prior art. See Topological dark matter in the literature and Topological defects and the vacuum manifold.
Topological defect; homotopy group. A wall, line or point where a field that has broken a symmetry is held out of its vacuum, because the vacuum values around it cannot be joined smoothly: a domain wall, a string or a monopole, according to whether the vacuum manifold has separate pieces (π₀), loops that cannot be shrunk (π₁) or spheres that cannot be shrunk (π₂). See Topological defects and the vacuum manifold.
Topological loophole. The route Debt 3 leaves open: a single topological object whose own structure would localize it in momentum. It is untested and, since the soliton candidate’s retirement, has no candidate; #11 does not say consistently whether it is still a work item. See Open: the topological loophole.
Toy-model note. papers/reciprocity-toy-models.md, the note that builds the two toy models, graded B in round 4 and revised to version 2; its worklog is notes/toy-lagrangian.md. See Toy models of broken reciprocity.
Toy-model scripts. The four scripts verify/toy_coset.py, verify/toy_gw.py, verify/toy_s4.py and verify/toy_s5.py, which recompute the toy-model note’s results in the gate. See The toy-model scripts.
Toy models. Two small, fully specified field theories built to test the hard core in isolation and to meet acceptance criterion 1: model I and model II. See Toy models of broken reciprocity.
Transfer cross-section. σ_T, the measure of self-scattering that weights each collision by the fraction of forward momentum it removes, so that grazing collisions count for little; quoted per unit mass for dark matter. See The transfer cross-section σ_T.
Trilemma. The handoff’s word for the three-way dark-sector question of #11 v2.0, χ particles, an X-condensate or solitons, reduced to two candidates when the soliton candidate was retired. See Dark-sector candidates and Row 11: particles or condensate (OP9).
“True but irrelevant”. The idea that conjugate monopoles might exist yet affect nothing observable. By P4 they gravitate, so #11 §11.1 calls the case “the empty set” and Appendix A item 5 “measure zero”, a correction supplied by P.R. See Conjugate monopoles as ontology.
Tuning test. Whether the potential that gives X its mass is free of the Boulware–Deser ghost, that is, lands in the ghost-free class of Fierz–Pauli, de Rham–Gabadadze–Tolley and Hassan–Rosen; the verdict is a conditional pass. See The tuning test.
Turnaround. The far-future halt and reversal of our expansion once τ’s potential goes negative; by a·ã = 1 it is the conjugate bounce. Whether the potential as written can go negative is unresolved (flag 27). See The turnaround as the conjugate bounce and Row 5: the fate of the expansion.
Twisted element. ρ combined with the flip K → −K, an element of model I’s symmetry group that leaves the vacuum unchanged and acts on H exactly as ρ does; so the breaking of ρ has physical effect only once matter couples to the sign of K. See The twisted element ρ∘(K → −K).
Two gravitational charges. A chat-only claim that gravity has two independent charges: stress-energy, the source of the massless graviton, and dual stress, the source of X. See Two gravitational charges and the conjugate field equations (chat-only).

U#

Ultra-faint dwarf (UFD). The faintest dwarf galaxies, the densest, oldest and most dark-matter-dominated systems known. See Dwarf galaxies: cores and ultra-faint dwarfs.
Under pressure. #11 v2.1’s label for the dark-energy sector after the second data release of the Dark Energy Spectroscopic Instrument favoured a phantom crossing against the framework’s strict w ≥ −1; “under real pressure ahead of DR3”, in the root CLAUDE.md, where DR3 is Data Release 3. See DESI DR2’s phantom crossing.
Unified modular structure. #11 §11.3’s conjecture that the phase-space polarization and the charge-lattice polarization are parts of one enlarged modular structure, as T- and S-duality sit inside U-duality; open problem 8 (OP8). See Open: one modular structure for both polarizations (OP8).
Unimodularity. The corollary det H = 1 of the compatibility theorem: the phase-space volume H measures cannot change, which the program reads as the constancy of Planck’s constant built into the geometry. See Corollaries: unimodularity, no B-field, slaved momentum metric.
Unitary equivalence; Noether symmetry; Stone–von Neumann theorem. By the Stone–von Neumann theorem the standard representations of the position–momentum commutation rules are all unitarily equivalent, so in ordinary quantum mechanics ρ is a change of description. The program needs ρ to be a Noether symmetry, one that leaves a specific action unchanged, since only such a symmetry can be broken spontaneously. See Unitary equivalence versus Noether symmetry.

V#

Vacuum; vacuum manifold; stabilizer. The vacuum is the lowest-energy state of a theory, or of the universe. When a symmetry is broken the vacua form a family, the vacuum manifold, and the symmetries that leave one chosen vacuum fixed form its stabilizer; the shape of the vacuum manifold decides which defects can form. See Topological defects and the vacuum manifold and Spontaneous symmetry breaking.
Vacuum-energy identity. Under the palindrome, the value of the bimetric potential at the aligned point is twice its tadpole, V(1) = 2T, so a flat aligned vacuum forces the spin-2 interaction sector’s vacuum energy to zero. It says nothing about the vacuum energy of matter loops, and whether it is new awaits the partially-massless comparison. See The vacuum-energy identity V(1) = 2T.
Vacuum slice. The values of the modular field with X = 0, where Z = i·g; there the compatibility theorem’s block form, and with it the slaved momentum metric, still holds. See The modular field Z = X + iY.
Velocity dispersion σ. The spread of the velocities of a system’s stars or particles about their mean, the standard deviation along one direction, in km/s; in equilibrium it is set by the system’s mass and size. In the program it is the scale the velocity gate is measured against: where σ is below the gate velocity v*, as in dwarf galaxies, most pairs of particles interact. See The velocity dispersion σ.
Velocity gate. The factor that turns conjugate matter’s self-interaction off between particles approaching with a large relative velocity. The scattering amplitude depends, through a form factor F(k²/μ²), on the incoming relative momentum, a variable that, according to #11, no carrier local in position produces. In signal terms, an ordinary contact force acts where two waveforms overlap, and the gate acts only where their spectra overlap as well. See The velocity gate.
Velocity-space granularity. The lab notebook’s prediction, its old row 3, that a relaxed galaxy halo splits into of order ten broad velocity streams whose gravity leaves correlated ripples along cold stellar streams; withdrawn permanently, on both islands. See Obituary: velocity-space granularity in halos (old row 3).
Verdict; verdict A, B, C. Collision. In blind review, the referee’s grade. The skeptic console’s prompt defines the scale: A “coherent speculative physics that uses established results correctly”, B “flawed but containing salvageable ideas”, C “confabulation”. B is “flawed but salvageable” in the handoff and both pre-registrations, and C “fundamentally flawed” in the round-3 referee’s verdict; no round has returned A. The tuning test’s verdict, a conditional pass, is unrelated. See The blind-review protocol and verdict scale and The skeptic review console.
Verification battery (T1–T7). verify/battery.py: seven numerical and exact-integer tests of the matrix algebra at the core of the program, from the compatibility theorem and the modular parametrization to the algebra behind X’s mass and the vacuum-energy identity, mostly evaluated at randomly drawn sample points. #11 calls what it confirms Tier 1 and tags it [V]. Unrelated to the † literature battery. See The verification battery T1–T7.
Vielbein; frame field. A set of local reference axes, orthonormal by definition, from which a metric is built quadratically; the program calls frames first-order variables and metrics second-order ones. Hinterbichler and Rosen wrote the ghost-free potentials for two spin-2 fields as wedge products of two frames. See Vielbein formulation and wedge potentials.
Vlasov equation. The equation of a gas whose particles interact only through a smooth, averaged force field, so that the gas is fully specified by how densely it fills position and velocity. See Vlasov stability and Landau damping.

W#

W′ overclosure; minimal sector. The result that the simplest version of the soliton candidate’s hidden sector, with no particle lighter than its heavy W′± bosons carrying hidden charge, is excluded: the stable W′± would outweigh the observed dark matter 10¹⁶ to 10¹⁷ times. It forced the hidden fermion ψ, and it survives the candidate. See W′ overclosure: the minimal sector is excluded.
Wave dark matter. Dark matter made of particles so light that many share each quantum state, so that a halo behaves as a classical wave field. See Wave dark matter.
Wave island. The range of very light χ masses, roughly 3×10⁻¹⁹ eV to 10⁻⁴ eV, in which a halo of conjugate matter is a classical wave field; gated attraction can drive condensation there, so collective clumping is possible but never required. See The wave island.
Wave kinetics. The theory of how a field of many random-phase waves relaxes as the waves scatter off one another, building Bose-star cores; Levkov, Panin and Tkachev (LPT) worked it out for gravity, and Debt 3 added a gated channel. See Wave kinetics and Bose-star formation.
Wedge sector; wedge polynomials. The bimetric potential written as wedge products of the two frames, the Hinterbichler–Rosen form, ghost-free by construction. That the program’s potential takes this form was selected, not derived from S_H; deriving it is open problem 1 (OP1). See Vielbein formulation and wedge potentials and Open: deriving the wedge sector from S_H (OP1).
Weyl semimetal; Berry-curvature monopole. Crystals whose electronic bands carry monopoles of Berry curvature in momentum space: the one laboratory analog of momentum-space monopoles that row 8 names. See Row 8: no monopoles of our sector and Conjugate monopoles as ontology.
Wigner function; Weyl symbol. A drawing of a quantum state as a distribution over phase space, whose sums over all momenta and over all positions give the position and momentum probabilities; unlike a probability, it can be negative. Weyl symbols turn operators into functions on phase space in the same way. See The Wigner function and Weyl symbols.
Withdrawn. The status of #14 after round 3: “Kept as the audit trail; not for circulation.” See The soliton candidate (retired) and Obituary: superheavy conjugate solitons.
Witten effect. A monopole in a theory with a nonzero vacuum angle θ acquires an electric charge, θ/2π of the unit charge for each unit of magnetic charge, which makes it a dyon; with kinetic mixing it would give the retired candidate’s hidden monopoles a small visible charge (round-3 ruling 9), a channel strict sector separation closed. See The Witten effect and Kinetic mixing between sectors.
Worklog. Collision. The v3 worklog, review/v3-worklog.md, records the revision of #14 between rounds 2 and 3; the toy-model worklog, notes/toy-lagrangian.md, records the building of the toy models. See Obituary: superheavy conjugate solitons and Toy models of broken reciprocity.
Worklog labels. R1–R7, F1, F2, L1 and O1–O3 in the v3 worklog; F1–F6 and C1–C3 in round 4. Collision: F1 and F2 name different findings in the two. See Review rounds 1 and 2 and Review round 4.

X#

X-condensate. A coherent, spatially uniform oscillation of the massive momentum graviton X, proposed as the dark matter; one of the two remaining candidates, which would make dark matter and the hidden half of the geometry one field. See The X-condensate candidate.
x-polarized; p-polarized; x-tilted. Organized around position, or around momentum. Ordinary matter is x-polarized and conjugate matter p-polarized (P4); our vacuum is x-tilted, and its mirror would be organized around momentum (P5). See P4: polarized matter and strict sector separation and P5: the vacuum selects a polarization.

Y#

Yukawa force; range; Yukawa coupling. Collision. A Yukawa force is the force carried by a massive particle, which dies away beyond a range of order the inverse of the particle’s mass. X’s force is of this kind, so its gravitational-strength effects are confined to short distances, where experiment does not constrain them. A Yukawa coupling is a different object: the term that joins a scalar field to a fermion and, through the Higgs field’s vacuum value, gives the fermion its mass; the toy models use it as an analogy for how a choice of vacuum can make matter’s interactions local. See Yukawa forces and their range, its section on the name collision, and Safety by range: X and ordinary matter.

Collisions#

Words that mean different things in different documents or sections, each explained in its entry above:

Appendix A — the battery code in HANDOFF.md, or the supposition audit in #11;
battery — the verification battery T1–T7, or the † literature battery;
benchmark — the scattering benchmark of conjugate matter, or the withdrawn soliton benchmark;
Born — Born reciprocity and its family of terms, or the unrelated Born approximation of scattering theory;
branch — Branch R, Branches (i) and (ii), or the palindromic branch;
condensate — the χ condensate on the wave island, the X-condensate, the monopole condensate of confinement, or model II’s condensed levels;
conjugate — the program’s momentum-side counterparts, conjugate variables, or charge conjugation;
criterion — acceptance criterion 1, the success criteria S0–S5, the mean-field criterion, or the health criterion for X;
dual — the program’s momentum-side counterparts, or the electric–magnetic sense of the dual superconductor;
duality — Born duality, electric–magnetic (S-) duality, Seiberg duality, the Langmann–Szabo duality, scale-factor duality, or the duality dictionary;
flag — an item of review/wiki-build-flags.md, or calc note #3’s degeneration flag;
frame — a vielbein, a duality frame, the dual or conjugate frame, a force-free frame, or the polarization frame;
the gate — the velocity gate, or scripts/check.sh;
island — the particle and wave islands of Debt 3, or the consistency islands of #7 and #11 §15;
misalignment — the relic-production mechanism, or the potential that gives X its mass;
phase — phase space, a thermodynamic phase, an angle (the Maslov phase, model II’s β), or a phantom phase;
polarization — a choice of Lagrangian subspace, model II’s Δ(β), or the ordinary polarization of waves;
rows — #11 §13’s numbering, or the lab notebook’s older one;
self-dual — Z = i and the circle |Z| = 1, Ω = 1, #13’s Planck closure, or Born’s self-dual program;
soliton — a Bose-star core (#3, #4), or a topological defect (#14, #11 §12);
spectrum — a waveform’s momentum description, or a theory’s list of particles and masses;
tier — claim tiers, metric and frame tiers, the toy-model worklog’s tiers of criteria, or the conjecture tier of the handoff and #13;
verdict — a referee’s grade, or the tuning test’s conditional pass; and verdict C in particular — “confabulation” in the skeptic console, “fundamentally flawed” in round 3;
worklog — the v3 worklog, or the toy-model worklog;
Yukawa — the force of a massive mediator, or the coupling that gives fermions their masses;
F1, F2 — different findings in the v3 worklog and in round 4.

Symbols with several meanings (ρ, ω, τ, μ, H, K, X, f, Λ and others) are listed on Notation.

Acronyms#

The acronyms used on the wiki’s pages, with the expansions of the registry scripts/wiki-acronyms.txt:

The program and its sources. BBT — Broken-Born, the program (the lab notebook’s title says Broken-Born Theory); FLM — Freidel–Leigh–Minic; LMW — Liveoak–Maharana–Wells; LPT — Levkov–Panin–Tkachev; GW — Grosse–Wulkenhaar, so gravitational waves are always written out; OP1–OP11 — the open problems of #11 §14; PDG — Particle Data Group; LLM — large language model.
Physics in general. GR — general relativity; SR — special relativity; QM — quantum mechanics; QFT — quantum field theory; QED — quantum electrodynamics; QCD — quantum chromodynamics; QG — quantum gravity; SM — Standard Model; SSB — spontaneous symmetry breaking; EFT — effective field theory; SUSY — supersymmetry; SYM — super Yang–Mills; CP — charge conjugation and parity; BCS — Bardeen–Cooper–Schrieffer; BKT — Berezinskii–Kosterlitz–Thouless; MC — Monte Carlo.
Gravity. FP — Fierz–Pauli; HR — Hassan–Rosen; PM — partially massless; DFT — double field theory.
Dark matter and astrophysics. DM — dark matter; CDM — cold dark matter; SIDM — self-interacting dark matter; WIMP — weakly interacting massive particle; UFD — ultra-faint dwarf; MW — Milky Way; GC — globular cluster; LSB — low surface brightness; MCP — millicharged particle.
Cosmology. DE — dark energy; DESI — Dark Energy Spectroscopic Instrument; DR1, DR2, DR3, DR4 — its Data Release 1, Data Release 2, Data Release 3 and Data Release 4; BAO — baryon acoustic oscillations; CMB — cosmic microwave background; CPL — Chevallier–Polarski–Linder; BBN — Big Bang nucleosynthesis; FLRW — Friedmann–Lemaître–Robertson–Walker; NEC — null energy condition; LIGO — Laser Interferometer Gravitational-Wave Observatory; LAT — the Fermi Large Area Telescope.
Monopoles and duality. DSZ — Dirac–Schwinger–Zwanziger; BPS — Bogomolny–Prasad–Sommerfield; KZ — Kibble–Zurek; MACRO — Monopole, Astrophysics and Cosmic Ray Observatory.

Sources#

papers/broken-born-checkpoint-v2.md §1–§15 and Appendix A — the current meaning of nearly every program term, the tags, the claim tiers, the open problems OP1–OP11 and the predictions table
papers/reciprocity-toy-models.md §1–§6 — the toy models’ vocabulary: model I and model II, the twisted element, the ρ-preserving and bounded potentials, the frozen-H reduction, the ordered ℤ₂ phase, quantum restoration, covariance
papers/conjugate-special-relativity.md §1–§7 — the vocabulary of conjugate special relativity, including “closure at the self-dual point” and “conjecture-tier”
CLAUDE.md “Since the handoff”, “Method” and “Working with Paul” — the queue, “lead”, the strong form of locality, the verification rules, “go”, the attribution line, the metaphors that do not work
HANDOFF.md §2–§8 — the artifact numbers, ✓, the chat-only results and “conjecture tier”, the electric-sublattice clause, the trilemma, the review history, the prose register
notes/broken-born-theory.md — Born’s debt, the cliff, the old rows, the debts, the v0.1 action, the original postulates, the soccer-ball problem
notes/broken-born-program-v1.md — #9, the first consolidation
notes/debt3a-stream-stability.md, notes/debt3b-wave-island.md, notes/debt3c-ufd-endpoint.md — the Debt-3 vocabulary: islands, patch modes, co-movers, “spent”, Scenarios A and B, Branches (i) and (ii), the mass drain, the gravothermal self-limit, the degeneration flag
notes/debt1a-geometric-core.md, notes/debt1a-ii-X-classification.md, notes/debt1a-iii-tuning-test.md, notes/debt1a-iv-beta-coefficients.md — Branch R, the nontriviality theorem, the self-dual circle, the symplectic partner, the metric and frame tiers, the palindrome and the tadpole
notes/knot-dark-matter-standalone.md §1–§6 — the retired candidate’s vocabulary: hypothesis H, exclusion conditions, requirements, acceptance criteria, “not for circulation”
notes/toy-lagrangian.md — the success criteria and their two tiers, the weak and strong forms of S5
review/v3-worklog.md — the worklog labels R1–R7, F1, F2, L1 and O1–O3
review/round3-adjudication.md, review/round4-adjudication.md — rulings, decisions, lessons, “program-native”, “benchmark-conditional”, the ordered ℤ₂ phase
review/skeptic-review-console.html — the console’s A/B/C verdict scale
review/wiki-build-flags.md items 7, 16, 23, 27, 28, 33 and 43 — the flags the entries point to
popsci/universes-other-half.md — “the second geometry”, the magnetic identification
scripts/wiki-acronyms.txt — the acronym expansions
wiki/CLAUDE.md — the wiki’s status vocabulary, title markers and folded headings