The Broken-Born program

The Broken-Born program (BBT) is a speculative physics research program built on one symmetry of quantum mechanics, Born reciprocity. Position and momentum are related as a waveform and its spectrum, and the basic rules of quantum mechanics, before any force law is specified (its kinematics), are unchanged when the two are exchanged, with one change of sign. In 1938 Max Born asked why the rest of physics treats them so unequally. The program takes the exchange as an exact symmetry of the laws that the vacuum, the universe’s lowest-energy state, breaks spontaneously, as the aligned spins of a magnet break the rotational symmetry of the laws that govern them, and follows the consequences into gravity, dark matter, dark energy and electric–magnetic duality. Its founding image, dark matter clumping in velocity rather than in space, was ruled out by the program’s calculations, and a later review retired one of its three dark-matter candidates. What stands is a chain of structural results on its geometry and gravity, the two remaining dark-matter candidates (particles and a condensate), and a dark-energy prediction under pressure from current data. In its own words it is a Lakatosian research program, not a theory: in the philosopher Imre Lakatos’s sense, a body of work built on a fixed core assumption, whose surrounding claims are revised as tests come in, and judged by whether those revisions keep producing new predictions.

Stands: the hard core, reciprocity exact and spontaneously broken, with P2′, the postulate that leaves the vacuum, not the laws, to choose which directions count as position; the conjugate universe as a second description of one state; the modular field Z, one complex field whose parts are read as the spacetime metric, a second gravitational field and the dark-energy field; the polarization as a Goldstone angle: in both toy models, the split into position and momentum is chosen along a continuous angle; why the second graviton X must be massive; the palindrome in X’s interaction coefficients and the vacuum-energy identity that follows from it, whose novelty is under audit; the gated scattering law of conjugate matter; the net theorem that clumping is nowhere mandatory; the two dark-matter candidates, χ particles and the X-condensate; the dark-energy field τ and its bound w ≥ −1, both under pressure from the second DESI data release; the symplectic charge lattice; the maximum force of conjugate special relativity, unreviewed; rows 1–10 of the predictions table, with row 5’s premise unresolved (flag 27 in review/wiki-build-flags.md); every entry in Claims that stand. · Died: velocity clumping, the founding image, killed in Debt 3, with the prediction rows withdrawn with it (velocity-space granularity in halos and Fornax friction suppression) and Scenario A, the version for wave-like dark matter in which the same attraction also makes the cores of dwarf galaxies; conjugate collapse powering our expansion, dead twice; monopoles as the explanation of their non-detection; the superheavy soliton candidate, retired after review round 3, and the parts of it that died with it or before it: the coupling α_d ≈ 34 via Dirac quantization, its hidden-sector model as a proposal of the program’s own, the Kibble normalization of its abundance, Planck-suppressed mixing of its hidden photon with ours, the mass window of its light fermion ψ and a chat-only bound on its abundance, the √N topological floor; the naive ρ-preserving potential of the first toy model, unbounded below once all its fields are dynamical; and the magnetic identification, a claim of the popular article #12 only; every entry in the graveyard. · Open: first in the work queue (root CLAUDE.md): the partially-massless comparison (OP2) of the vacuum-energy identity with the literature, the † literature battery (OP10) of source checks on every reference cited from memory, and a note on the phase-space diameter relation, a chat-only conjecture; the word “theory” waits on OP1–OP3: deriving X’s interaction potential (the wedge sector) from first principles (OP1), the partially-massless comparison and Lorentzian dressing (OP3), the extension of results proven for positive-definite metrics to the signature of spacetime; the checkpoint’s other open items: the gate shape (OP4), the dual-stress enhancement (OP5), τ–Stückelberg mixing (OP6), polarization-genesis and the 5.4 : 1 ratio of dark to ordinary matter (OP7), one modular structure for both polarizations (OP8) and telling particles from a condensate (OP9); the open ends of the toy Lagrangian (OP11), whose acceptance criterion is met in the referees’ wording: a Monte Carlo with H dynamical, the origin of the ρ-preserving potential, forced locality and, as a lead, the real model’s one-loop preference; open outside the checkpoint’s list: the field content of the broken vacuum, whether ρ’s SO(2) breaks in the coupled model, stability at equal Planck masses, the topological loophole, dual kinetic energy versus τ’s potential, the sign of V(τ) and the turnaround, the two dual cones and the four-dimensional Born map; every entry, with the open sub-questions folded into other pages and the full queue, in Open problems and the queue. · Superseded: the statements replaced by the two forced corrections to the hard core (#11 §15): the original P2, which froze too much of the background geometry and gave way to P2′, and the heuristic dictionary w_eff = −2 − w̃, which gave way to w_eff = −w̃; the lab notebook’s v0.1 action and its geometric term S_H; and earlier forms kept on the pages that replaced them, such as the exponential cliff of v0.1, now the knee, and the discrete breaking pattern, now the Goldstone angle; every entry in Superseded statements. · Conjectures: results that exist only in the original claude.ai conversation (chat-only): two gravitational charges and the conjugate field equations, the phase-space diameter relation and momentum-space black holes; claims found only in the popular articles (popsci-only), such as “a single assumption” and “constant is impossible”, which never decide a status; every entry in Conjectures.

The program in brief#

Checkpoint #11’s technical abstract (papers/broken-born-checkpoint-v2.md §1, version 2.2), point by point with the tags it carries, followed by two later additions the abstract leaves out: the pressure from current dark-energy data recorded in v2.1 (§10) and the toy models of v2.2 (§4, §10, §14 item 11).

  • The symmetry and its breaking. Born reciprocity, ρ: (x, p) → (p, −x), is an exact symmetry of quantum kinematics, implemented unitarily by the Fourier transform (#11 §3). The program takes it as exact and spontaneously broken. Consistency forces only the symplectic form ω, the antisymmetric pairing of position and momentum whose rigidity is the constancy of ℏ, to be rigid, with the neutral metric η, the structure that splits phase space (positions and momenta taken together) into position and momentum, emergent as the order parameter: postulate P2′ [P], a correction forced by the nontriviality theorem [D].
  • One geometric field. The geometric sector organizes into a modular field Z = X + iY on the Siegel domain Sp(2d, ℝ)/U(d), the space of all phase-space metrics compatible with ω: Im Z is the spacetime metric, Re Z = X a second symmetric tensor, reciprocity acts as Z → −Z⁻¹, and the Lagrangian Grassmannian Λ(d), the space of all ways to split phase space into position and momentum and the home of the dark-energy field τ, is the domain’s distinguished (Shilov) boundary.
  • A massive second graviton. A chain of structural results — a compatibility theorem [T][V], the multi-graviton no-go [8†], a signature obstruction, and an explicit tuning test [V] — forces X to be a massive spin-2 field, a second graviton with a mass, in the interchange-symmetric branch of Hassan–Rosen bimetric gravity [10†, 11†], with the second frame confined to Λ(4).
  • Zero wedge vacuum energy. A four-line identity [V] shows that a flat aligned vacuum forces the wedge sector’s vacuum energy to vanish exactly; the wedge sector is the frame-built interaction potential that gives X its mass. The branch is adjacent to, and contains, the partially-massless parameter point [24S]. The identity does not by itself address matter-loop vacuum energy (#11 §7.3).
  • Dark matter. Conjugate matter, the counterpart of ordinary matter organized around momentum, survives as gated self-interacting dark matter whose gate is X-exchange: its self-interaction acts only between particles moving at nearly the same velocity (the velocity gate). Collective momentum-space clumping is proven non-mandatory everywhere and falsified where it would have been mandatory. A third candidate, superheavy topological solitons of a hidden gauge sector, was retired after an execution-verified review found its abundance estimate misnormalized, “leaving two candidates: particles and a condensate”.
  • Charge lattices. The electric–magnetic charge lattice, with its Dirac–Schwinger–Zwanziger symplectic pairing [17†], is a second arena in which the same polarization choice recurs: choosing which charges count as electric is the same mathematical operation as choosing which coordinates count as position.
  • Dark energy, under pressure (v2.1). τ is hilltop quintessence, a dark-energy field whose energy density may fall as space expands but never rise: its equation of state w, the ratio of pressure to energy density, obeys w ≥ −1 strictly. The Dark Energy Spectroscopic Instrument’s Data Release 2 (DESI DR2) favors a phantom crossing, with w below −1 further back than redshift z ≈ 0.4, so “the dark-energy sector is under real pressure ahead of DR3” (Data Release 3; root CLAUDE.md).
  • Toy models (v2.2). In an explicit ρ-symmetric coset model of the phase-space metric H and the real structure K, and in the complex self-dual Grosse–Wulkenhaar model, ρ sits inside a continuous U(1), so the polarization is a Goldstone angle [D][V] rather than a discrete choice. A definite polarization needs a ρ-preserving potential, whose derivation is open. The referees’ standing demand for an explicit symmetric action is met in their wording. In #11’s words, “None of this tests the cosmology; it only shows the structure is consistent” (§10).

Bracketed numbers such as [8†] are entries in #11’s reference list, collected with the other bibliographies on References. The entry behind [24S] has no authors, and its title is a description rather than the paper’s title (flag 9 in review/wiki-build-flags.md, confirmed by the flags’ audit).

Who made it#

The program was developed with Claude on claude.ai in September–October 2026 and continues in this repository (root CLAUDE.md). Paul (P.R.), an independent developer, supplies conjecture and direction and holds a veto; Claude (Anthropic) supplies derivations, counterexamples, verification and drafting. The attribution line for papers (root CLAUDE.md; HANDOFF.md §7) reads: “conjecture and direction, P.R.; derivations, counterexamples, verification, drafting, Claude (Anthropic).” Paul cannot independently verify most of the technical physics. He relies on the provenance tags, the machine checks and the review verdicts predicted in writing before each round (pre-registration) to tell sound results from confabulation, which is why every page states its status and its sources. The wiki itself was drafted by Claude from the documents and checked against them by separate verifiers working in fresh context (the wiki’s build). See The collaboration.

Reading a page#

  • Shape. Every page opens with an italic passage for a reader without physics, then a Status: line (the status in words, the tags, and what verifies the claim or where it was decided), then the technical record and a list of sources.
  • Status. Each page has one: established (literature), alive (a program claim that currently stands), conjecture, open, dead (killed, and stays dead), superseded, method, record or hub (a section index). Titles mark status: Obituary: … for a dead claim, Open: … (OPn) with the checkpoint’s open-item number where it has one, … (superseded), … (chat-only), … (popsci-only), and Row n: … for a prediction. A minor item of another status inside a page, such as an open sub-question on a standing claim, gets its own section headed Open: …, Superseded: …, Chat-only: …, Popsci-only: … or Conjecture: …, and the registers link that section.
  • Provenance tags (#11’s header): [D] derived in this program; [T] established literature; [P] postulate; [O] open; [V] machine-verified. Citation marks: [S], retrieved by live search during the project; †, cited from model memory, to be verified against the source before external use. Pages copy tags exactly from their sources and never upgrade one; an explanation of established physics written from general knowledge is [T], and any citation it adds is †. See Provenance tags and citation marks.
  • Variants in the sources. HANDOFF.md marks machine checks with ✓, and one of them, on the Debt-3 shortfall, has no script behind it (flag 16 in review/wiki-build-flags.md); #13 qualifies its tags ("[D — structural]"); the toy-model note carries no tags, because it was written for blind review, and uses † for the Hermitian adjoint rather than as a citation mark.
  • What [V] means. A script in verify/ reproduces the arithmetic. It does not show that the physics is right: “a verification script confirms arithmetic, not the model it encodes” (#11 §2). The scripts run in scripts/check.sh; see Verification.
  • When sources disagree. The wiki follows a fixed precedence, most current first: the root CLAUDE.md (“Since the handoff”), then #11 v2.2 and the toy-model note v2, the review adjudications, #13, HANDOFF.md, the notes, and the popular articles last. The popular article #12 presents the framework as if it were confirmed and never decides a status. Disagreements that no source settles are stated, not resolved. See Status of the program’s claims and Conflicts between sources.
  • Suspected errors in the sources. Where the wiki’s verifiers believe a source states something wrong, the page quotes the source as written and points to a numbered flag in review/wiki-build-flags.md (“see flag 23”); no page corrects a source. The file holds 44 flags. Flags 1–43 were re-checked by independent agents told to refute them. Of flags 1–42, 32 were confirmed, 8 depend on a convention or a reading the documents support, 2 are unclear because they rest on model memory, and none was refuted; flag 43 was confirmed by two independent checks. Flag 44, a minor point of wording raised after the audit, is not yet audited. Every flag still awaits Paul’s ruling; the pending rulings list them with their verdicts and flag 44’s audit status. A flag that involves arithmetic has an executed check in review/wiki-build-checks/, which is not part of verify/ or the gate.

Reading paths#

Map#

The sections follow the program’s argument in the order checkpoint #11 builds it, then the tests, the registers, the method and the record.

  1. The research program — the question Born asked, the hard core, the postulates P1–P5, the conjugate universe, the founding suppositions and their fates, the referees’ main critique (“the framework does no work”) and the program’s self-assessment. It comes first because every later section follows from the postulates.
  2. Phase-space geometry — the arena the postulates are written in: Born reciprocity and Born geometry as established physics, including the compatibility theorem, then the program’s modular field Z. Its theorems are proven for positive-definite metrics, and their extension to the signature of spacetime is open.
  3. Spontaneous breaking of reciprocity — the mechanism of the hard core: established symmetry-breaking theory, then the program’s order parameter, the Goldstone angle, the open origin of the potential, matter locality, and the two toy models that realize the breaking.
  4. Gravity and the momentum graviton — established massless and massive spin-2 physics, then the results of Debt 1, the program’s name for its missing field equation for momentum-space geometry: why X must be massive, the tuning test of the potential that gives X its mass, and the palindromic branch with its vacuum-energy identity.
  5. Dark matter — established halo and wave-dark-matter physics, then conjugate matter and its velocity gate (Debt 2), the death of momentum clumping (Debt 3), and the candidates: two standing, one retired.
  6. Cosmology — Friedmann cosmology, the constraint a·ã = 1 between our scale factor and the conjugate one, the duality dictionary, dark energy as the polarization angle τ under pressure from DESI DR2, and early-universe physics as background.
  7. Electric–magnetic duality and charge lattices — monopoles and dualities as established physics, then the program’s monopole audit, the symplectic charge lattice, the conjecture of one modular structure for both polarizations, and a popular-article claim recorded as dead.
  8. Conjugate special relativity — special relativity and the maximum-force literature as the established template, then the kinematics of the momentum polarization from #13: a second light cone, in time and momentum, whose limiting rate of change of momentum is a maximum force. It follows the checkpoint’s sectors because it is a separate paper, which #11 v2.2 does not mention; #13 tags most of its results [D], and no review or script has checked them.
  9. Predictions and kill conditions — one page per row of #11 §13: the standard expectation, the framework’s requirement and the result that would kill it, with the history of the table. The tests come after the sectors whose derivations they test.
  10. Status of the program’s claims — the registers: the graveyard first, then the claims that stand, the open problems and the queue, the conjectures, and the superseded statements.
  11. Method — Lakatos’s methodology of research programmes as the established frame, then how the program works and checks itself: the collaboration, provenance tags and claim tiers, the open † literature battery, the rule that negative results are reported prominently, verification (the iron rule of no arithmetic by eyeball, independent anchors, the gate, and one page per family of scripts) and blind review with pre-registration.
  12. History — the dated timeline, including this wiki’s build and its flags file, the three debts that organized the early work, and the documents #1–#15 with their order of precedence and the conflicts between them.
  13. Glossary — the program’s terms and those of the physics it uses, in plain words, with collisions flagged.
  14. Notation — the symbols across the documents, their collisions and the convention the wiki uses.
  15. References — every work the documents cite: the bibliographies of the checkpoint, #13, #14 and the toy-model note, and the literature the worklogs and referees retrieved, with each work’s † or [S] mark.

Boundaries#

The wiki explains and indexes the program’s documents — the papers, notes, review records and verify/ scripts — and adds no results. Every number on a page is copied from a source document or a verify/ output, and when the wiki and a source disagree, the source wins (wiki/CLAUDE.md). The documents themselves are described under Documents; the check that keeps the wiki’s links, sources and page shapes consistent is part of the gate.