Open problems and the queue

This register lists the problems the Broken-Born program has not yet solved and the order in which work on them is queued. Its core is the eleven numbered open problems of checkpoint #11, the program’s current reference, which says that none of them is any longer about whether the structure can exist. Around that list it collects the current work queue, the open ends of the toy models, the open problems raised in the notes, the reviews and the other papers, and the open sub-questions recorded on pages about other subjects. #11 says the word “theory” still waits on three of the numbered problems: deriving the interaction potential of the program’s second graviton from its geometric action, comparing a vacuum-energy identity with the literature on partially massless gravity, and extending proofs made for positive-definite metrics to the signature of spacetime. The register ends with the 44 suspected errors in the source documents recorded while this wiki was built. Independent agents, each told to refute a flag, then re-checked the first 43. Of the first 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, added later, was confirmed by both of its two checks. Flag 44, a minor point of wording raised after the audit, has not yet been audited. Each still awaits Paul’s ruling.

Status: Record, a register current to flag 44, the last item of review/wiki-build-flags.md, which the file marks as not yet audited; it dates the audit of flags 1–42 and flag 43’s own audit 2026-10-22 — no tags of its own; each item keeps its source’s tag, and the numbered items carry [O] in #11 §14 — the numbered list is #11’s (papers/broken-born-checkpoint-v2.md §14), the queue is the root CLAUDE.md’s, which supersedes HANDOFF.md §8, and the pending rulings are the 44 items of review/wiki-build-flags.md, each with its audit verdict where it has one.

An open problem with a page of its own is titled “Open: …”, with its #11 number (OPn) when it has one. A smaller open question recorded on a page about another subject sits under a heading of the form “Open: …” on that page, and this register links that heading. Items tagged [O] carry the open tag in their source; the others are open because no document resolves them.

The checkpoint’s open items (#11 §14)#

#11 §14 says that none of its list is any longer “about whether the structure can exist”, and #11 §15 says that the word “theory” “still waits on items 1–3”. Two of the eleven, items 2 and 10, are on the current queue; the others are unscheduled.

  1. Open: deriving the wedge sector from S_H (OP1) — the ghost-free interaction potential of the momentum graviton X, the frame-tier wedge class, was chosen by minimality and consistency rather than derived from the geometric action S_H: “class selected, not derived” [O]. The same gap in the language of the modular field is Open: the Re Z sector of the geometric action (OP1), where calc note #5 restates the field equation for momentum-space geometry as the Re Z sector of S_H. One of the three items “theory” waits on.
  2. Open: the partially-massless comparison (OP2) — a detailed comparison of the palindromic branch with partially massless (PM) bimetric gravity, asking “is reciprocity the origin of the PM symmetry?”, and a “Convention-careful check of the vacuum-energy identity against [24S, 25S]” [O]. Until it is done the identity is presented as adjacent to known results, not as new. Current queue item 1, and one of the three items “theory” waits on. The reference [24S] is the subject of flag 9 below.
  3. Open: Lorentzian dressing of the Euclidean skeleton (OP3) — the compatibility theorem, the Siegel parametrization and the chain that forces X to be massive are proven for a positive-definite phase-space metric; extending them to the signature of spacetime, where the group that leaves the vacuum fixed becomes non-compact, is open [O]. First flagged in calc note #6 §3, and one of the three items “theory” waits on. Flag 30 notes that #13’s two causal cones depend on it; the audit rates that flag as depending on a tagging convention.
  4. Open: the gate shape (OP4) — whether the gate that switches off conjugate matter’s self-interaction at large relative velocity falls off as a Gaussian or with a power-law (rational) tail, which depends on the X propagator along the momentum directions; “now observable” in the tail of the self-interaction knee [O]. #11 §15 counts “gate tail not yet forced” among the program’s degeneration risks.
  5. Open: the dual-stress enhancement (OP5) — why conjugate matter can scatter off itself with a nuclear-scale cross-section while ordinary matter couples to X only at gravitational strength; #11 §8 calls it the “Main open quantitative item” [O].
  6. Open: τ–Stückelberg mixing (OP6) — how strongly the dark-energy field τ mixes, through the potential, with the modes that X absorbs when it becomes massive; calc note #8 §3 logged the mixing as “expected small by compactness”, and no document computes it [O].
  7. Open: polarization-genesis and the 5.4 : 1 ratio (OP7) — no mechanism yet sets the observed ratio of dark to ordinary matter, Ω_χ : Ω_b = 5.4 : 1, the program’s counterpart of baryogenesis [O]; #11 §12: “The 5.4 : 1 abundance question (polarization-genesis) applies to both” remaining candidates.
  8. Open: one modular structure for both polarizations (OP8) — whether the vacuum’s choice of which directions count as position and the choice of which charges count as electric are components of “one enlarged modular structure”, the conjecture of #11 §11.3 [O]. The item adds: “The soliton-spectrum and p-localization items are closed by the §12 obituary.” An older related clause is listed under electric–magnetic duality below.
  9. Row 11: particles or condensate (OP9) — telling the two remaining dark-matter candidates, χ particles and an X-condensate, apart through rows 1–3 of the predictions table and signatures of a coherent field [O]; a diagnostic row with no kill condition.
  10. Open: the † literature battery (OP10) — checking every reference cited from model memory (†) against its source [O]. #11’s footer reads “not for submission until the † audit (open item 10) completes”. Current queue item 1. Flags 20 and 32 below are items for it; flag 9 concerns a live-searched reference and falls outside it.
  11. Acceptance criterion 1: the toy Lagrangian (OP11) — “Met in the referees’ wording” by the coset model of (H, K) with a bounded ρ-preserving potential. “Still open [O]: a Monte Carlo with H dynamical; a derivation of the potential; locality of matter beyond the weak (Yukawa-like) form, which in the toy reduces to P4” (Open: the parts not yet met). The open ends have their own section below.

The work queue#

Current (root CLAUDE.md)#

  1. HANDOFF.md §8 items 5–7: the partially-massless comparison (OP2), the † literature battery (OP10), and the phase-space-diameter note, a write-up of a chat-only conjecture listed among the conjectures.
  2. Optional: a round-5 review of the toy-model note, “but only before any external use”. The last review of the note was round 4.

The root CLAUDE.md drops HANDOFF.md §8 item 3 and gives its reasons in the “Decisions” section of review/round3-adjudication.md. No other open item is queued, including the open ends of the toy Lagrangian.

The handoff’s queue and what became of it (HANDOFF.md §8, superseded)#

  1. Cut v3 of #14 — done; v3 failed the round-3 review with verdict C and was withdrawn (Review round 3).
  2. Re-run the execution-verified blind audit — done, as round 3.
  3. The √N-floor freeze-out estimate — dropped: its premise is inverted, and it has no candidate left to serve (round-3 Decision 3; Obituary: the √N topological floor).
  4. The toy Lagrangian — “done to the referees’ wording” (root CLAUDE.md); its open ends are listed below.
  5. The partially-massless comparison — current queue item 1.
  6. The literature battery — current queue item 1. The same item’s other task, resolving the gravity-induced kinetic-mixing question, was overtaken by strict sector separation (round-3 Decision 1; P4).
  7. Optional write-ups — the phase-space-diameter note is current queue item 1; LaTeX and arXiv shaping were to wait until items 1–5 were done.

The toy-model open ends#

The root CLAUDE.md lists four open ends of the toy Lagrangian: a Monte Carlo with H dynamical; a derivation of the ρ-preserving potential; the strong form of matter locality; and the real Grosse–Wulkenhaar model’s one-loop preference for the position-sharp vacuum, “a lead”. The first three are the parts of acceptance criterion 1 that #11 §14 item 11 still lists as open. The toy-model note’s own “Not shown” list (papers/reciprocity-toy-models.md §6) covers the same four and adds two, and its §4 leaves one comparison undone.

  1. A Monte Carlo with H dynamical. Open: a Monte Carlo with H dynamical — the ordered ℤ₂ phase has been simulated only with the metric field H frozen; for the full model there is only a classical check that the vacuum is a minimum with all four field directions free.
  2. A derivation of the ρ-preserving potential. Open: the origin of the ρ-preserving potential — a definite polarization needs a potential that keeps reciprocity as a symmetry but pins the polarization angle; it brings in “a rigid, unordered pair of axes”, more fixed structure than postulate P2′ provides, and nothing derives it.
  3. The strong form of matter locality. Open: forced locality and the P4 lock — no mechanism forces matter to interact through a coupling built from H and the order parameter K, so in the toy, locality in position comes from postulate P4, packaged with a momentum-local mirror sector, rather than being derived; the worklog adds that the question is “also open in the literature”.
    • Open: locality is assumed, not derived — the argument that the breaking is mandatory runs from locality to a selected polarization; the toy models test the converse and find only its weak form.
  4. The real model’s one-loop preference, “a lead”. Open: the real model’s one-loop preference (a lead) — in the real-field Grosse–Wulkenhaar model the first quantum correction gives the vacuum sharper in position the lower free energy, F(+) − F(−) = 2.634 at truncations N = 6, 8 and 10. The selection is explicit, not spontaneous, it holds at fixed bare μ², and “the large-N, renormalized fate of the real model’s one-loop selection” is not shown (note §3, §6; round-4 finding F4).
  5. Whether ρ’s SO(2) breaks in the coupled model. Open: does ρ’s SO(2) break in the coupled model? — in two dimensions the compact polarization angle cannot order by itself (the Mermin–Wagner–Coleman theorem), but model I’s metric sector is a hyperbolic sigma model, which can; whether the coupled model breaks ρ’s SO(2) without a potential is open (round-4 point C2; note §6).
  6. Anything beyond d = 1. Both toy models take a phase space with one position and one momentum direction, d = 1, and “anything beyond d = 1” is not shown (note §6). The worklog’s untested remark on 3+1 dimensions is listed among the conjectures.
  7. The comparison with the exact solution. Open: the comparison with the exact solution — the note names Langmann, Szabo and Zarembo’s exact solution of a related model as the check on quantum restoration in the complex model: “The exact solution of the related model [8] is the natural independent check. We have not carried it out.” (§4). Round 4’s revision 4 had asked for the comparison, yet the adjudication and the worklog record every accepted revision as applied (flag 42, confirmed by the audit). The note’s §6 also lists the restoration itself under “Shown (each by executed code)”, though it rests on §4’s analytic argument and verify/toy_gw.py checks only its premise (flag 41, confirmed by the audit). Both flags are listed under the pending rulings below.

Four pages collect several of these open ends as they bear on their own subject:

Open problems outside the checkpoint’s list#

These items are open in the record but are not among #11 §14’s eleven, and none is on the current queue. Most were raised in the calc notes, the lab notebook, the reviews or #13 and are not in #11’s current list; two were found when the sources were read side by side for this wiki.

Phase-space geometry#

  • Open: field content of the broken vacuum — once the vacuum has chosen a polarization, the geometry leaves the ordinary metric, X, the dark-energy field τ, nine further moduli and matter; whether inverse-Higgs constraints remove the nine was never worked out (calc note #5 §D, §F item 4).
  • Open: connection uniqueness under P2′ — Freidel, Rudolph and Svoboda proved the Born connection unique for the full triple (ω, η, H); whether ω and H alone fix it is item 5 of calc note #5 §F, and it was not carried into #11 §14.
  • Open: a mechanism that selects one section — the double-field-theory literature either selects the pair of null sections or uses outside input, and nothing picks one of the two; the toy’s section condition “confines matter to one null line without telling the two apart” (toy-model note §5; worklog chunk 4).
  • Open: extensivity (the soccer-ball problem) — why the large total momenta of everyday bodies do not probe the curvature of momentum space; the lab notebook’s sixth open problem [O] (#1 §11), dropped from later lists without a resolution.

Spontaneous breaking of reciprocity#

  • Open: the section condition on curved backgrounds — “consistency of the section condition on general backgrounds is open there and open here” (#1 §2) [O]; no later document takes it up, and the toy models, set in flat phase space, do not reach it.

The open problems of the toy models are listed in their own section above.

Gravity#

  • Open: stability at equal Planck masses — the analysis that finds a heavy spin-2 field linearly stable at late times assumes that the second metric’s Planck mass is much smaller than the first, while reciprocity forces the two to be equal: “Whether a large mass alone is enough at M_f = M_g is open” (review/v3-worklog.md, round-2 item R7).

Dark matter#

  • Open: the topological loophole — a single topological object might localize in momentum, a case that the collective calculations of Debt 3 do not test. #11 says both that the loophole “remains untested, but has no candidate” (§12) and that the “p-localization items are closed by the §12 obituary” (§14 item 8), and does not reconcile the two.
  • Open: calibration of the coefficient c — the coefficient of the wave-island condensation rate is heuristic, and its calibration against Levkov–Panin–Tkachev numerics is “a flagged to-do” (calc note #3; #9 §10 item 8); #11 §9 marks the coefficients [O] but does not itemize the task.
  • Open: rows 1 and 2 in wave language — “Rows 1–2 must be re-derived in wave language” (calc note #2); calc note #3 supplies a wave form of the knee’s tail, and no document restates the isotropy of row 2 for a wave halo.
  • The relic abundance of particle χ — a light, strongly self-coupled sector connected to ordinary matter only by gravity “cannot freeze out thermally without cannibalism problems” (#1 §5.3; thermal freeze-out), so its abundance needs an asymmetry. It is part of OP7, polarization-genesis.

Electric–magnetic duality#

  • Open: the electric-sublattice clause — the handoff’s and #14’s wordings of acceptance criterion 1 asked the order parameter also to select the electric sublattice; the toy models that met the criterion contain no gauge field and no charge lattice, and nothing in the repository addresses the clause.

Cosmology#

  • Open: dual kinetic energy versus τ’s potential — the lab notebook motivates a near-constant dark energy as kinetic energy in the momentum-space description of the universe (#1 §6) and implements it as the potential energy of τ (#1 §7); no document derives one from the other.
  • Open: the sign of V(τ) and the turnaround — the documents write V = V₀[1 + cos(τ/f)], which is never negative for V₀ > 0, yet the far-future turnaround needs V < 0; no document reconciles the two (flag 27, confirmed by the audit, which found no reading of the documents that removes the conflict).

Conjugate special relativity#

  • Open: the two dual cones — #13 §1 builds the momentum-space light cone in time and momentum with slope c̃, while §6 calls E = c|p| the dual null cone, which by the worklog’s analysis belongs to the unbuilt four-dimensional map; raised by Paul on 2026-10-19 as worklog item O3, with the instruction to settle which construction governs before any paper claims more.
  • Open: the four-dimensional Born map and dual dynamics — the construction that also exchanges time and energy, and the field equations of the momentum polarization that it would allow (#13 §6–§7) [O].
  • Open: the factor of 4 — between #13’s maximum force c⁴/G and the literature’s c⁴/4G; first among #13 §7’s open items [O], and nothing is computed on it.
  • Open: merger-band corrections — “whether merger-band gravitational-wave data can bound dual-kinematic corrections” (#13 §7); the arena is “flagged, not derived” (#13 §2) [O].
  • Open: which clocks respond — #13 §3 restricts force dilation to conjugate-polarized systems and leaves the rest open: “which physical clocks respond is polarization-dependent, O”. The question is missing from #13 §7’s own open list, from #11 §14 and from the queue.
  • Open: the invariant length against the checkpoint’s kinematics — #13 §4 labels conjugate quanta by an invariant length λ instead of a mass, while #11 §8 describes χ in ordinary kinematics; worklog item O3: “The papers were never reconciled.” #11 governs for the χ candidate, and the item is unscheduled.

Pending rulings#

review/wiki-build-flags.md lists 44 suspected errors in the source documents. The verifiers found flags 1–42 while this wiki was built; flag 43, added on 2026-10-22, concerns where the program’s thawing corridor lies relative to the phantom crossing in Data Release 2 (DR2) of the Dark Energy Spectroscopic Instrument (DESI); and flag 44, raised the same day by the verifier of the signature obstruction, concerns the wording of a standard result in calc note #6. The wiki quotes each source as written and corrects none of them; every item needs Paul’s ruling. Flags 1–42 were then re-checked by independent agents told to refute them, two for each of the eleven mathematical flags (one defending the source, one recomputing from scratch) and one for each of the rest. The file dates that audit 2026-10-22 and gives each of these flags its verdict: 32 confirmed, 8 that depend on a convention or a reading the documents support, 2 unclear because they rest on model memory, and none refuted (review/wiki-build-checks/flag-audit.json). Flag 43 came with its own audit, two independent checks, one defending the documents and one recomputing from scratch, and both confirmed it (review/wiki-build-checks/corridor/). Flag 44 was raised after that audit, and the file marks it not yet audited: it has had one check, the page verifier’s symbolic check that the kinetic term of its exception is not invariant under the full linearized diffeomorphisms, and no independent refuters. Where arithmetic is involved, the verifier’s executed check is kept in review/wiki-build-checks/, and the auditors’ scripts in its audit/ folder, outside the gate; a ruling that accepts a flag should add the check to verify/. One line per flag follows, with its verdict, or for flag 44 its audit status, and the page that discusses the statement.

Where to start, the file’s own list, in its order, by consequence for the program’s claims:

  • Flag 27 (confirmed): the turnaround needs V(τ) < 0, but the stated potential V₀[1 + cos(τ/f)] has minimum 0 for V₀ > 0 (#11 §10, #9, #1 §7); either an offset is missing or the turnaround needs another mechanism, which bears on row 5 and on the dark-energy over-constraint, and the audit found no reading of the documents that removes the conflict (Open: the sign of V(τ) and the turnaround).
  • Flag 43 (confirmed): the program’s thawing corridor wₐ ≈ −1.5(1 + w₀) (#11 §10, #1 §7 item 2, #9 §8) lies in the region w₀ > −1, w₀ + wₐ < −1 of the w₀–wₐ plane, in which a line of the Chevallier–Polarski–Linder form passes below −1 in the past and in which DR2’s fits lie, and no document says so; fields with the program’s potential that never fall below −1 also give fits there, and what separates the corridor from DR2’s crossing is the slope (a crossing at redshift z = 2 against z ≈ 0.4), not the region. The file says this “bears on how row 4’s pressure is stated, not on whether it exists” (the corridor and DR2’s crossing).
  • Flag 23 (confirmed): #11 §6 and §10 identify the cosmological constraint a·ã = 1 with the |Z| = 1 locus; the check finds a·ã = 1 along the whole imaginary axis at X = 0, which meets |Z| = 1 only at Z = i. The identification also appears in calc note #5 §C, #1 addendum v0.3 and HANDOFF.md §2 (the cosmological constraint).
  • Flag 39 (depends on a convention or reading): #11 states two actions of ρ on the spin-2 sector, the frame exchange g ↔ f of §7.3 (with calc note #8 §1, #1 addendum v0.6 and #9 §5) and §6’s Z → −Z⁻¹, and they give the massless graviton opposite parities; the parities of #8 §3 and #11 §7.5 hold under the frame exchange, which the palindrome also needs, and not under §6’s map if the graviton is read as the fluctuation of Im Z (two actions of reciprocity).
  • Flag 3 (confirmed): calc note #7 gives the zero set of the misalignment potential as “X = 0 and Y = Y⁻¹”; the verifier’s check finds it larger (at d = 1 the whole self-dual circle |Z| = 1, not only Z = i), which leaves a flat direction at quadratic order; a ruling is needed on whether this is intended and whether it affects the vacuum structure (the misalignment potential).
  • Flag 6 (confirmed): “By symmetry rather than tuning” (#1 addendum v0.6, #10) overstates the vacuum-energy identity, since the flatness condition V(1) = T is itself one condition on the βₙ; #11 §7.3’s “by symmetry” is to be checked against it, and the phrase recurs in #11’s plain-language passages (§1, §7), #9 §5 and the closing sentence of calc note #8 §2 (the vacuum-energy identity).
  • Flag 1 (confirmed): calc note #5 §B, echoed in #11 §5 and #9 §3, calls the polarizations that are Lagrangian for ω and null for η “discrete”; for d ≥ 2 they form continuous families, though the conclusion, no Maslov circle and so no τ, survives (the nontriviality theorem).
  • Flag 33 (confirmed): verify/soliton_obituary.py says it recomputes every number the round-3 record quotes, but it does not check the referee’s numbers in rulings 3 and 4 or ruling 6’s figure, among six computed figures for the candidate that the audit counts as never recomputed (what it does not check).
  • Flag 34 (confirmed): verify/soliton_obituary.py calls its constants “PDG and Planck 2018 values”, PDG being the Particle Data Group, without its predecessor’s caveat that they come from model memory; the values are typed in, not retrieved (the soliton-obituary script).
  • Flag 42 (confirmed): the round-4 adjudication and the toy worklog record every accepted revision as applied, but the toy-model note v2 §4 says of the Langmann–Szabo–Zarembo comparison that revision 4 asked for, “We have not carried it out.” (review round 4).
  • Flag 41 (confirmed): the toy-model note §6 lists the complex model’s “restoration under quantization” under “Shown (each by executed code)”, but the result rests on §4’s analytic argument, and verify/toy_gw.py checks only its premise (quantum restoration in the complex model).
  • Flag 5 (confirmed): #11 §7.5 and #9 write M_X ∝ 2(β₁+β₂), though the β combination fixes the squared Fierz–Pauli mass, as their source, calc note #8 §3, writes it; notation only (spectrum, parameters and reciprocity parity).
  • Flag 28 (confirmed): #11 §11.2 writes our magnetic coupling as 4π/e² ≈ 34; with α = e²/4π that expression is 1/α ≈ 137, while e·g = 2π gives 1/(4α) ≈ 34.26, so the number is right and the formula beside it is not (the convention behind 34).

The other thirty-one, which the file describes as wording, pointers, dates and references, in numerical order:

  • Flag 2 (confirmed): the toy-model note §5 calls the coupling I “odd in K”, but I ≥ 0, so it is only not invariant under K → −K (locality from an (H, K)-built coupling).
  • Flag 4 (confirmed): calc note #7 §2 expands S as “S = 2h + x² + O(3)”, omitting a term −h²; the quadratic Fierz–Pauli test, which uses only S ≈ 2h, is unaffected (the metric tier fails twice).
  • Flag 7 (confirmed): #11 §7.1’s “the unique consistent structure” drops calc note #6 §3’s qualifier, “exactly one known consistent structure”; #6 §5, #9 §5 item 3, #11 §15 and HANDOFF.md §1 also drop it, and #7 §5 keeps it (why X must be massive).
  • Flag 8 (confirmed): calc note #8 §3 says “five-function freedom” for five constant coefficients βₙ, which would be “five-parameter” (constrained bimetric gravity).
  • Flag 9 (confirmed): #11’s reference [24S] (arXiv:1609.09515) has no authors, and its title is a description; being live-searched, it falls outside the † battery, and the audit names the paper as Apolo, Hassan and Lundkvist’s (the partially-massless comparison).
  • Flag 10 (confirmed): smaller pointers and wordings: #1 §1 points to §5 for the dark-energy potential, which is in §3 (the lab notebook); the toy-model worklog lists “ρ sits inside a continuous U(1)” as unpredicted although its predictions anticipated the restored U(1) (success criteria); verify/toy_s5.py part C still says “built from K” (the (H, K)-built coupling); and the round-4 referee’s audit notes use “boost” for two different families (review round 4).
  • Flag 11 (depends on a convention or reading): the model-II tadpole grows as “ln N” in the toy-model note v2 §4 and as 2 ln N in the round-4 referee’s notes and the adjudication, and verify/toy_gw.py checks only one harmonic series; the audit found the difference one of normalization, the tadpole holding two equal harmonic sums; recorded as conflict C29 (quantum restoration in the complex model).
  • Flag 12 (confirmed): review/round4-adjudication.md calls the zero mode of V_b an “exact” squeeze symmetry; a symbolic check finds V_b not squeeze-invariant away from K = ±K_ref, and the wiki follows the note v2’s “not symmetry-protected” (the bounded potential V_b).
  • Flag 13 (confirmed): the toy-model note’s ⟨|m|⟩ = 0.954 ± 0.0001 “at every size” is a conservative bound; verify/toy_s4.py prints ± 0.0000 at L = 64 (Monte Carlo: an ordered ℤ₂ phase).
  • Flag 14 (depends on a convention or reading): calc note #7 §2’s “Tr(g²) = p₄ of the square-root eigenvalues” holds for the eigenvalues of √(f⁻¹g), not for the √(g⁻¹f) that the bimetric potentials use, and #7 fixes neither the root nor the measure; the conclusion, outside the eₙ span (battery T7), stands (elementary symmetric polynomials).
  • Flag 15 (confirmed): calc note #6 §2’s phrase “η antisymmetric-pairing vs ω” reads as calling η antisymmetric; η is the symmetric neutral metric and ω the antisymmetric form (the symplectic partner of the graviton).
  • Flag 16 (confirmed): HANDOFF.md §2 marks the Debt-3 shortfall “fails by 10²⁸–10³¹” as machine-verified, but no script in verify/ checks it, and #11 §9 tags it [D]; the verifier’s recomputation reproduces it and could be moved into verify/ (the mean-field criterion).
  • Flag 17 (depends on a convention or reading): calc note #6 §4 writes the gate as e^{−(p₁−p₂)²/2μ²} and #1 §3 as e^{−k²/μ²}, which differ by √2 in μ only if #6’s form is read as the gate on the amplitude; read as the factor on the rate it matches #1, so #13 §4, which combines #6’s fiber width with #1’s v*, is consistent under the documents’ convention, and no stated number changes (the velocity gate).
  • Flag 18 (unclear, rests on model memory): #1 §8 dates the “maturity” of baryogenesis to 1966, while Sakharov’s conditions are usually dated 1967 (model memory, †, unchecked) (polarization-genesis).
  • Flag 19 (depends on a convention or reading): calc note #2’s classicality corollary evaluates the broad-gate formula at Milky Way conditions, which #2 itself treats as the narrow-gate regime; read as a ceiling on the mass, as #11 §9 uses it, the corollary is right, and read as the Milky Way’s threshold it is about 3× high; the occupation number is much greater than 1 either way (the classicality theorem).
  • Flag 20 (confirmed): #11’s reference [23]† gives the title and journal of “Bigravitational origin of dark matter” with the arXiv number of its companion paper, “Heavy spin-2 Dark Matter”; found by live search, and an item for the † battery (bigravity dark matter).
  • Flag 21 (confirmed): round-3 ruling 3 credits the referee’s Kibble–Zurek integration with “1e9–1e12 overproduction”, but the integration gave 1.1e12–2.2e12, and the lower end comes from the Liveoak–Maharana–Wells analytic estimate; the verdict is unaffected (round-3 verdict and rulings).
  • Flag 22 (confirmed): #14 gives Planck’s N_eff interval as “2.99 +- 0.34”, where the round-3 referee’s audit records +0.34/−0.33; the bound uses only the upper side, so nothing changes (the hidden sector’s thermal history).
  • Flag 24 (confirmed): the chat-only diameter relation is “square exactly at the bounce” without saying which bounce; if the turnaround is meant, the rectangle would be most elongated there (the phase-space diameter relation).
  • Flag 25 (confirmed): #1 §1 (P2) and §4 cite “§7” for the cosmological constraint, which #1 derives in §6 (the cosmological constraint).
  • Flag 26 (confirmed): HANDOFF.md §2 calls the third data release of the Dark Energy Spectroscopic Instrument “three-year data”, but the second release already covers three years of operations, as a live search found (DESI baryon acoustic oscillations).
  • Flag 29 (confirmed): #13 §1 and §6 cite #11 §7 for X’s effect being “in momentum”, which #11 §7 does not say; its “Yukawa-cut at 1/M_X” is a range in position, and the momentum reading appears only among the chat-only results (two causal cones).
  • Flag 30 (depends on a convention or reading): #13 §1 tags the block form from which it reads its two causal cones “[D — compatibility theorem]”, but that theorem’s metric is positive-definite and has no null cone, so the cones need the Lorentzian dressing, which is OP3; the tag itself sits on H = diag(g, g⁻¹), which the theorem gives, and whether #13’s inherited caveat covers the untagged cones is a question of tagging convention (two causal cones).
  • Flag 31 (depends on a convention or reading): #1 §4 puts quadratic photon dispersion “~10 orders below current sensitivity” with no script behind it; the audit retrieved the bound of the Fermi Large Area Telescope by live search [S] and found the figure loosely right counted in orders of the energy scale (8.0–8.6) and wrong counted in the size of the effect (14.5–17) (row 9: no linear photon dispersion).
  • Flag 32 (unclear, rests on model memory): CMB-S4, the cosmic microwave background experiment that #11 names as the probe for row 10, may have lost its United States funding in 2025; a lead from model memory (†), unchecked, and an item for the † battery (row 10: an early step in G_eff).
  • Flag 35 (confirmed): review/round3-preregistration.md line 5 cites HANDOFF.md §6 for the 2-for-2 pre-registration record, which is in §5 (pre-registration and its calibration record).
  • Flag 36 (confirmed): verify/battery.py’s docstring and #11 §7.2 place the figures “66.58 vs 63.72” in #11 §2, which does not print them; they are in HANDOFF.md §5 (the verification battery).
  • Flag 37 (confirmed): README.md still describes the program as explaining “missing magnetic monopoles”, an explanation that HANDOFF.md §2 and #11 §11.1 list as dead (CLAUDE.md and the README).
  • Flag 38 (confirmed): the root CLAUDE.md says “#11 is now v2.1” where the file is v2.2, and its Layout names two of the six scripts that scripts/check.sh runs; its Layout and the header of scripts/check.sh also place arbitration scripts in verify/ and the gate, while those of rounds 3 and 4 sit in review/, unrun (CLAUDE.md and the README).
  • Flag 40 (depends on a convention or reading): the root CLAUDE.md’s round-4 lesson says round 4 “found a potential that was bounded only at frozen H”; with only H held at 1 and K free on its hyperboloid, the naive potential is unbounded below at the gated couplings λ = μ = 1, so the sentence is right only for the documents’ frozen-H reduction, which also keeps K on its circle K(φ), or for λ ≥ 4μ (the frozen-H reduction).
  • Flag 44 (minor, not yet audited): calc note #6 §2 states that “Without the gauge invariance, no ghost-free two-derivative kinetic term for a Lorentz-covariant symmetric tensor exists”; read literally, the full linearized diffeomorphism invariance is not needed, since a kinetic term invariant only under the transverse diffeomorphisms, those generated by a divergence-free vector field, and the Weyl rescalings, shifts of the field proportional to the metric, is also free of ghosts, as in linearized unimodular gravity. That smaller symmetry is still a gauge symmetry, so the conclusion that X must be gauged is unaffected and only “the gauge invariance” overstates; the two references the flag gives are from model memory (†) (what it assumes).

History of the register#

  • The lab notebook (#1 §11, version 0.1) listed six open problems “in order of severity”. The field equation for H became Debt 1, closed structurally by calc note #8; for the gate, the mechanism was found (X exchange, addendum v0.3) while the shape stays open as OP4; the stream-instability growth rate was answered negatively by Debt 3 (addendum v0.2); polarization-genesis is now OP7; the relic abundance closed only on the wave island, by misalignment production (addendum v0.2); extensivity dropped out of later lists and is listed above.
  • The program v1.0 (#9 §10) listed eight, including the X-condensate as the dark matter itself, tagged “[O — direction, deliberately unopened]”, and a set of literature verifications; “theory” waited on its items 1–2.
  • The calc notes’ residue. Calc note #8 §5 closed Debt 1 structurally with an open residue, “none of it existential”: the wedge reduction, the Lorentzian dressing, τ–Stückelberg mixing, the dual-stress enhancement and a literature check on Λ = 0. These are now OP1, OP3, OP6, OP5 and OP2.
  • The handoff (HANDOFF.md §2, “Open (the real frontier)”) listed eight. The toy Lagrangian is now met in the referees’ wording, though its wording there also asked η to select “the electric sublattice”, which nothing addresses (see the electric-sublattice clause above). The strong-coupling freeze-out and the √N floor went with the soliton candidate; kinetic mixing was addressed by taking P4 strictly (round-3 Decision 1); the partially-massless comparison, the wedge reduction, the Lorentzian dressing, the gate shape, the dual-stress enhancement and polarization-genesis carried over; the three-way candidate question became OP9 with two candidates.
  • The checkpoint (#11 §14) lists eleven. Version 2.1 closed the soliton-spectrum and p-localization items with the §12 obituary, and version 2.2 recorded item 11 as met in the referees’ wording.
  • The wiki’s build added the pending rulings. review/wiki-build-flags.md, begun on 2026-10-21, grew to 42 items, and the audit, which the file dates 2026-10-22, gave each item its verdict; flag 43 followed on 2026-10-22 with its own audit, and flag 44 the same day, not yet audited (the flags file on the timeline).

Sources#

  • CLAUDE.md “Since the handoff” — the current queue; the toy-model open ends; the dropped queue item 3.
  • papers/broken-born-checkpoint-v2.md §14, §15, §12, §8, footer — the eleven items; “theory” waits on items 1–3; the loophole statement; the main open quantitative item; the submission gate.
  • papers/reciprocity-toy-models.md §3, §4, §6 — the real-model lead, the unperformed comparison, the “Shown” list’s label on the restoration (flag 41) and the “Not shown” list.
  • review/round3-adjudication.md “Decisions” — strict P4, the candidate retired, the √N floor dropped, the toy Lagrangian next.
  • review/round4-adjudication.md “Rulings”, “Revisions for v2 of the note” — finding F4 and the SO(2) point; revision 4 and the heading that records every revision as applied (flag 42).
  • papers/conjugate-special-relativity.md §2, §3, §6, §7 — #13’s open items.
  • HANDOFF.md §2, §8 — the handoff’s open list and ranked queue.
  • review/wiki-build-flags.md — the pending rulings, items 1–44, with the audits’ verdicts, flag 44’s audit status and the file’s “Where to start” order.
  • review/wiki-build-checks/flag-audit.json — the audit’s verdict on each of flags 1–42, with its summary and evidence.
  • review/wiki-build-checks/README.md — the verifiers’ executed checks and, in review/wiki-build-checks/audit/, the auditors’ scripts and outputs; in review/wiki-build-checks/corridor/, the scripts and outputs of flag 43’s two checks.
  • notes/debt1a-iv-beta-coefficients.md §3, §5 — τ–Stückelberg mixing logged; the Debt-1 residue.
  • notes/debt1a-geometric-core.md §D, §F — the inverse-Higgs question; connection uniqueness.
  • notes/broken-born-theory.md §2, §5.3, §6, §7, §11 and addendum v0.2 — the original six items and their fates.
  • notes/broken-born-program-v1.md §10 — the v1.0 list of eight.
  • notes/debt3a-stream-stability.md, notes/debt3b-wave-island.md — rows 1–2 in wave language; the calibration to-do.
  • notes/toy-lagrangian.md “Chunk 4”, “Write-up and review” — strong locality “also open in the literature”; the section-selection verdict; “v2 applies every accepted revision” (flag 42).
  • review/v3-worklog.md “Round-2 pending list”, “New open items” — items R7 and O3.
Backward Claims that stand Conjectures: chat-only and popsci-only claims Forward