Conflicts between sources

The program’s documents were written over several weeks, and the later ones correct, re-tag or retire what the earlier ones said, so the same question can get different answers in different files. This page collects those disagreements between documents, and between two statements of the same document. Most are settled by a fixed order of precedence in which the most current document wins. The rest are cases where documents of equal standing disagree, or where no document addresses the point; for those the wiki reports both readings and does not choose. Suspected errors inside a single statement, such as a slip in a formula or a wrong section pointer, are listed separately for Paul’s ruling.

Status: Record, current to 2026-10-21 — untagged — the order of precedence is set in wiki/CLAUDE.md, with the root CLAUDE.md “Since the handoff” first; each entry names the documents that disagree and the document or rule that settles the point, or says that nothing does.

How disagreements are settled#

The wiki follows the most current document, in this order (wiki/CLAUDE.md; Documents):

  1. the root CLAUDE.md, section “Since the handoff” (CLAUDE.md and the README);
  2. checkpoint #11 v2.2 and the toy-model note v2 (the checkpoint; toy models);
  3. the review adjudications, review/round4-adjudication.md and review/round3-adjudication.md;
  4. #13 (conjugate special relativity);
  5. HANDOFF.md, whose §2 soliton candidate and §8 queue are superseded (the handoff document);
  6. the notes: the calc notes #2–#8 are final for their own scope, #1 and #9 are superseded as reference, and #14 is withdrawn (the lab notebook; the Debt-3 notes; the Debt-1 notes);
  7. the popular articles, never a source for a claim’s status (the popular articles).

Rules that go with the order:

  • Dead stays dead. Claims killed in HANDOFF.md §2, #11 §9 and §12, and the adjudications are reported as dead whatever a lower-ranked document says (the graveyard).
  • Tags are never upgraded. A claim carries the tag of the highest-ranked source. Where a document marks a statement as machine-verified but no verify/ script checks it, or checks only part of it, the wiki tags the unchecked part [D] (provenance tags).
  • Two statements inside one document. Where a top-ranked document says two different things, the wiki follows the more current or more specific statement, states the other, and lists the case here.
  • Unresolved means that documents of equal rank disagree, or that no document addresses the point. The page that holds the topic states both readings, and so does this one.

What this page does not list#

review/wiki-build-flags.md lists suspected errors inside single statements of the source documents, found while the wiki was built: arithmetic, formulas, section pointers and citations, each quoted faithfully on the wiki’s pages and awaiting Paul’s ruling, with executed checks in review/wiki-build-checks/. A flagged statement can recur in several documents that agree with one another, such as the reading of a·ã = 1 as the |Z| = 1 locus (item 23), and is then an error, not a conflict. Where an entry below concerns a flagged statement, it names the item.

The flags file and review/wiki-build-checks/README.md cite conflict numbers from the inventory compiled for the wiki’s build, which a reboot later cleared (recorded on the timeline). The numbers that survive in the repository are C20, C21, C27, C28, C29 and C54. The entries below give C20, C21, C27, C28 and C29; C54, a date in #1 (item 18), concerns a single statement and is left to the flags file.

Unresolved#

Cosmology#

  • The sign of τ’s potential (C20). #11 §10, #9 §8 and #1 §3 write V = V₀[1 + cos(τ/f)], which is never negative for V₀ > 0. The same documents need V < 0 for the turnaround: τ’s energy “eventually goes negative” (#11 §10), “A cosine potential is negative over half its range” (#1 §7), “Turnaround after V(τ) < 0 = conjugate bounce” (#9 §9, row 5), and the quintessence fits they cite use a negative minimum. No document notices the conflict or adds an offset. The executed check review/wiki-build-checks/v_sign_check.py prints that the potential’s minimum is 0; which statement the documents should carry awaits a ruling (review/wiki-build-flags.md item 27). → Open: the sign of V(τ) and the turnaround; the turnaround as the conjugate bounce; row 5; the over-constraint.
  • Dark energy as dual kinetic energy or as τ’s potential. #1 §6 finds that “the natural source of a near-constant dark energy is kinetic energy in the dual frame”; #1 §7 then identifies dark energy with τ “sitting near the top of its cosine potential”, and #9 and #11 keep the second picture. No document derives the link between the two, and no queue lists the gap. → Open: dual kinetic energy versus τ’s potential.

Dark matter#

  • The momentum-localization loophole, inside #11. §12: “The Debt-3 loophole — topological momentum-space localization of individual objects — remains untested, but has no candidate.” §14 item 8: “(The soliton-spectrum and p-localization items are closed by the §12 obituary.)” Read together, the logical loophole is untested, and it has no candidate and no work item; the wiki does not decide whether it is still a live question. → Open: the topological loophole; Obituary: superheavy conjugate solitons; Open: one modular structure for both polarizations.
  • The gate’s exponent. #1 §3 postulates e^{−k²/μ²}, with “k = m_χ v_rel/2 the incoming relative momentum”, and defines v* ≡ √2μ/m_χ (§5.1); calc note #6 §4 derives the overlap e^{−(p₁−p₂)²/2μ²} and calls it “the postulated gate”; #11 §8 writes F(k²/μ²) and fixes neither; #13 §4 combines #6’s fiber width with #1’s v* = √2 μ/m_χ. No source converts one exponent into the other. review/wiki-build-flags.md item 17 records a factor √2 in μ between the forms, with the check review/wiki-build-checks/gate_conventions.py; no stated number changes. The flag’s audit found the factor present only if #6’s form is read as the gate on the amplitude; read as the factor on the rate, it equals #1 §5.1’s with #1’s μ, and the audit rated the flag as depending on that convention. → the velocity gate; the gate mechanism; row 1.
  • The fuzzy end of Scenario B. Calc note 3b lets the cores come from “fuzzy-end quantum pressure at m ∼ 10⁻²² eV, or baryonic feedback”; calc note 3c later puts the lower edge of the surviving wave island at 3×10⁻¹⁹ eV, from the bounds on fuzzy dark matter. Neither note addresses the first option’s mass; baryonic feedback is unaffected. → Scenario B; bounds on fuzzy dark matter; the net theorem.
  • The occupation number’s normalization. Calc note 3b writes the per-mode occupation N_occ = ρ/(m⁴σ³) in its setup, as 3a does, and the “peak occupation N_occ ≈ (2π)^{3/2}ρ/(m⁴σ³)” in its rate, and reconciles neither with the other. At N_occ ∼ 10²⁰ the factor does not affect the classicality conclusion. → occupation number; the gated condensation rate; the classicality theorem.
  • Polarization-genesis and the nine heavy moduli. #1 §8’s sketch needs “the nine non-Maslov directions” to exist and decay at reheating; calc note #5 §D expects “inverse-Higgs constraints likely eliminate most [O]” of them, and lists their “inverse-Higgs accounting” as open (§F; inverse-Higgs constraints). No document reconciles the two. → Open: polarization-genesis; Open: field content of the broken vacuum.
  • The mediator mass and M_X. #1 §5.1 sets the benchmark with “a heavy transfer mediator (m_φ ≳ m_χ, contact-like in x)” and “m_φ ∼ m_χ”, before the gate’s carrier was identified as the momentum graviton X. #11 §8 keeps the amplitude with α̃ and m_φ, and no document relates either to the mass M_X of X or revisits the choice. → the scattering benchmark; Open: the dual-stress enhancement.

Gravity and symmetry breaking#

  • What X eats. Calc note #6 §3: “the four would-be Goldstones π_μ of the broken λ-gauge are eaten”; calc note #8 §3: the Higgsing “eats the vector π_μ and the longitudinal scalar of the λ-gradient sector”. #1’s v0.4 addendum and #11 §7.1 follow #6 (“X eats the four Goldstones”). No document reconciles the two wordings or relates them to the standard decomposition; both exclude τ from the eaten modes. → the gravitational Higgs mechanism; Goldstone modes and the Higgs mechanism; τ is not eaten; field content.
  • Which structure is “the real structure” (C27). #11’s P2′ writes η = HJ, “with the real structure J chosen spontaneously”, and #11 §5 defines J = η⁻¹H and K = η⁻¹ω. The toy-model note writes “A real structure K with K² = 1 and Kᵀ ω K = −ω defines a neutral metric η = ωK” (§1), and #11 §14 item 11 makes “η = ωK” the order parameter. Both documents rank 2. The check review/wiki-build-checks/jk_check.py finds that “η = HJ and η = ωK are the same matrix under #11 §5’s algebra”, so the clash is one of naming; the documents still differ in which operator they call the chosen structure. Pages on the toy models use K, pages on #11’s postulates J. → the order parameter; notation; the Lagrangian Grassmannian; model I: action and symmetries.
  • The tadpole’s coefficient in the complex Grosse–Wulkenhaar model (C29). The round-4 adjudication says the restoration argument “ignores the 2 ln N mass renormalization” (finding F6, “Accepted, not re-checked”) and asks to “add the 2 ln N mass renormalization” (revision 4); the toy-model note v2 says “The level-0 tadpole grows as ln N (it is a harmonic sum)” (§4); verify/toy_gw.py checks one harmonic series against ln N, while the referee’s one-loop tadpole sums both index orders, “2 sum_k (G_0k + G_k0)” (review/round4/referee/audit-notes.md). No document reconciles the coefficient (review/wiki-build-flags.md item 11). The note v2 is the higher-ranked statement, and both agree that the growth is logarithmic and that the no-breaking conclusion stands. → quantum restoration in the complex model.
  • “Consistency confines matter”. The toy-model note v2 says “So consistency confines matter to one null line without telling the two apart” (§5). The round-4 referee listed the phrase among the note’s over-reaches: “(iii) ‘consistency confines matter’ – the section condition is imposed, not derived, in this paper” (review/round4/referee/audit-notes.md, Step 3). The adjudication does not rule on the point, and its revisions do not mention it. The note’s wording stands, and the reading is unresolved. → the section condition.

Kinetic mixing#

  • Ceiling or floor. #11’s P4 writes “ε ≲ 10⁻¹³ [27S]”. The round-3 referee, reading the same paper of Gherghetta et al., notes that it presents 10⁻¹³ as a floor (the referee’s capitals), the “minimum kinetic mixing in any theory with hidden gauge interactions and charge symmetry breaking”, “consistent with “<~” only in the sense “up to”” (review/round3/referee/audit-notes.md, Step 1). #11’s wording stands; the reading is unresolved. → P4; kinetic mixing between sectors; row 7.

Electric–magnetic duality#

  • “The empty set” or “measure zero”. #11 §11.1: “’true but irrelevant’ is the empty set (a correction supplied by P.R.)”; #11 Appendix A item 5: “P.R.’s ’true-but-irrelevant is measure zero’”. The first says there is no such case, the second that such cases are negligible. The verdict is the same either way: as an explanation of the missing monopoles the idea is dead, and as ontology it is alive. → Obituary: conjugate monopoles explain the null result; conjugate monopoles as ontology.

Conjugate relativity#

  • The two dual cones in #13. #13 §1 uses the 3+1 construction, a cone in (t, p) with slope c̃; #13 §6 says “our massless dispersion E = c|p| is the dual null cone”, a cone in (E, p) with slope c that belongs to the four-dimensional Born map. The v3 worklog records the clash (item O3) and asks to “fix #13’s two cones and settle which construction governs (raised by Paul, 2026-10-19)”. #13 has not been revised, and no queue or open-item list schedules it. → Open: the two dual cones; two causal cones; Open: the four-dimensional Born map.
  • The dark sector’s kinematics. The same item: “#14 describes the dark sector entirely in our kinematics … #13 §4 labels conjugate quanta by an invariant length λ instead of a mass, and a λ = 0 quantum would sit on the dual null cone with |dp/dt| = c̃. The papers were never reconciled.” #11 §8 and §12 also treat χ in ordinary kinematics, with a mass m_χ. By precedence #11 governs for the χ candidate, and #13’s reading stays an unreconciled alternative. → the invariant-length shell; Obituary: the hidden SU(2) → U(1) proposal.

Method and records#

  • Arbitration scripts outside the gate. The root CLAUDE.md says of verify/: “arbitration and audit scripts go here”. The arbitration scripts of rounds 3 and 4, review/round3/adjudicator/round3_arb.py, review/round4/adjudicator/arb.py and review/round4/adjudicator/ctrl.py, sit in review/, and scripts/check.sh does not run them; the numbers they arbitrated are gated through verify/soliton_obituary.py and the toy-model scripts. No document says whether the instruction or the practice governs (review/wiki-build-flags.md item 38). → the gate; CLAUDE.md and the README.
  • The handoff’s review count. HANDOFF.md §1: “Three blind AI reviews returned verdict B (“flawed but salvageable”)”; its §6 records two completed rounds, “B / medium” and “B near B/C / medium”, and a third that was incomplete. No document reconciles the count. → the handoff document; review rounds 1 and 2; assessment.
  • The year of the Freidel–Rudolph–Svoboda theorem. #1 §2 cites “Freidel, Rudolph & Svoboda (2018)” and #9 §3 “[T: Freidel–Rudolph–Svoboda 2018]”; #11’s reference [7]† gives “Commun. Math. Phys. (2019), arXiv:1806.05992”. The difference may be an arXiv year against a journal year; the check is left to the † literature battery. → the Born connection; references; Open: the † literature battery.

Settled by precedence#

Status changes since the handoff#

  • The soliton candidate. HANDOFF.md §2 calls superheavy solitons the “Current best DM candidate” (DM: dark matter), its §8 items 1–3 serve it, #11 v2.0 listed it in a three-way “trilemma”, and #10 and #12 present the knots as live, #12 as the favored option. The root CLAUDE.md ("dead as a program-native proposal"), #11 §12 and round-3 Decision 2 outrank all of these: dead. → Obituary: superheavy conjugate solitons; its popsci-only corner.
  • Conjugate monopoles. HANDOFF.md §2 ties their ontology to the soliton candidate (“As ontology they’re alive (the soliton candidate)”). The ontology stands (#11 §11.1); the dark-matter candidacy is retired. → conjugate monopoles as ontology.
  • The handoff’s open items and queue. Item 1, the toy Lagrangian, is met in the referees’ wording; item 2, the √N floor, was dropped (Decision 3); item 3, kinetic mixing, is answered by strict P4 (Decision 1); item 8’s three-way question is now two-way (#11 §12). The queue of HANDOFF.md §8 is replaced by the root CLAUDE.md’s. → acceptance criterion 1; Obituary: the √N topological floor; dark-sector candidates; open problems and the queue.
  • The electric-sublattice clause. HANDOFF.md §2 asks for η as “the order parameter also selecting the electric sublattice”; #11 §14 item 11 and the toy work’s criteria omit the clause and declare the criterion met. The root CLAUDE.md wording governs (“done to the referees’ wording”), and the clause is recorded as unaddressed. → acceptance criterion 1; Open: the electric-sublattice clause.
  • The handoff’s statuses. #11 “v2.0 — CURRENT REFERENCE”, #14 “v2 — CURRENT blind-review manuscript”, round 3 “(incomplete)”, pre-registration “scored 2-for-2 on verdicts”, and the read order “#11 → #14 → §6 of this handoff → calc notes” are all overtaken: #11 is v2.2, #14 is withdrawn, round 3 returned verdict C, the record now reads miss and hit for rounds 3 and 4, and the root CLAUDE.md gives the read order. → the handoff document; pre-registration.
  • The version of #11 in the root CLAUDE.md. Its bullet “#11 is now v2.1” stands beside a later bullet citing “#11 v2.2 §14 item 11”. The checkpoint’s own header, “Version 2.2 (checkpoint), amended 2026-10-20”, decides its version (review/wiki-build-flags.md item 38). → CLAUDE.md and the README.
  • The real model’s one-loop lead. The root CLAUDE.md lists “the real Grosse–Wulkenhaar model’s one-loop preference for the position-sharp vacuum, a lead” among the toy Lagrangian’s open ends; #11 §14 item 11 does not mention it. Rank 1 governs, and the lead is recorded as open. → Open: the real model’s one-loop preference.

Tags, attribution and what the checks cover#

  • The compatibility theorem. #1 v0.3 (“a rigorous compatibility theorem”), #5 ("[D — rigorous]"), #9 ("[D]"), #11 v2.0 ("[D][V]"), HANDOFF.md §2 (✓) and #13 ("[D — compatibility theorem]") treat it as derived in the program, and #14 lists it as “Derived within the framework or by standard methods”. #11 since v2.1 tags it [T][V], crediting the statement to Freidel, Leigh and Minic, and the root CLAUDE.md records it as “re-tagged [T] (Freidel–Leigh–Minic)”; the block proof and the machine check stay the program’s. The round-3 audit adds that positivity is not needed for C = 0, so that step of #11 §5’s proof is redundant, not wrong. #13’s use of the theorem for its two cones is queried in review/wiki-build-flags.md item 30. → the compatibility theorem; two causal cones.
  • The referee’s form of the complex structure. The round-3 referee writes Freidel, Leigh and Minic’s statement as “B-field vanishes <=> I = H^-1 omega compatible” (audit notes, Step 3); #11 §5 defines I = ω⁻¹H. The wiki follows #11. → the structures ω, η, H.
  • The ✓ on 10²⁸–10³¹. HANDOFF.md §2 marks the clumping shortfall machine-verified, but no verify/ script computes it, and #11 §9 tags it [D] (review/wiki-build-flags.md item 16). → the mean-field criterion.
  • Statements phrased as if machine-checked. #11 §2 lists “det H = 1 across the whole family” among the Tier-1 checks, and §5 says it “— machine-verified — persists across the whole modular family”; the handoff describes test T2 as “det H = 1 off-vacuum”, and T2 checks one randomly drawn member. #11 §7.2 calls Tr(g²) + Tr(g⁻²) “provably outside the linear-in-eₙ span (T7)”, where T7 tests p₄ alone on random numbers. #11 tags §7.2 [D][V], while calc note #7 tags the frame tier “[D — structural, resting on T]” and no test covers it. The wiki tags the family-wide statement, the exclusion of Tr(g²) + Tr(g⁻²) and the frame tier [D]. → the verification battery; corollaries of the compatibility theorem; the metric tier fails twice; elementary symmetric polynomials; vielbein formulation.
  • Where the figures 66.58 and 63.72 are. #11 §7.2 refers to “the 66.58-vs-63.72 test of §2”, and the docstring of verify/battery.py says its printed figures “are the ones quoted in papers/broken-born-checkpoint-v2.md §2 (66.58 vs 63.72; rms 3.29)”. #11 §2 describes the test in words and prints only “rms residual 3.29”; the two figures are in HANDOFF.md §5, “66.58 vs 63.72 at seed 0”, and in the battery’s output (review/wiki-build-flags.md item 36). The wiki cites #11 §7.2 and test T4 for them. → the verification battery; the Fierz–Pauli mass term; the metric tier fails twice.
  • Novelty. Calc note #8 called the interchange-symmetric branch “an ad hoc simplification” that “now has a reason to exist”, and said the Λ = 0 property, if new, “is a standalone publishable observation”; #9 §11 counted “at least two results that stand on their own”. #11 §7.4 downgraded the claim from “likely standalone result” to “requires detailed comparison with the PM and exchange-symmetric literature”, PM being partially massless, and §15 counts “one identity awaiting a novelty verdict”. #11 governs. → Open: the partially-massless comparison; the palindrome; the symplectic partner.
  • “Exactly one known” structure. Calc note #6 §3: massive spin-2 “has exactly one known consistent structure”; #11 §7.1: “The unique consistent structure for massive spin-2”. The wiki quotes #11 as the current statement and points to review/wiki-build-flags.md item 7 for the dropped qualifier. → why X must be massive.
  • “Eighty-eight years in a drawer” (#10). #11 v2.2 §3 credits Freidel, Leigh and Minic for “broken Born duality”, and v2.1 §5 for the compatibility statement. → broken Born duality.
  • “Proved in 2000” (#12), for the multi-graviton no-go theorem, against #11’s citation of the 2001 journal paper, hep-th/0007220: the preprint year and the journal year of the same work, not a disagreement of substance. → the multi-graviton no-go theorem.

Gravity#

  • How many structural tests. Calc note #7 §5 counts “three structural tests in a row (multi-graviton no-go, signature obstruction, tuning test)”; #9 §11, HANDOFF.md §1 and #11 §15 count “four consecutive consistency tests”. The documents that name the four name them differently: #9 §11 gives the chain “no-go → Higgs → HR class → palindrome”, HR being Hassan–Rosen, while #11’s technical abstract lists “a compatibility theorem [T][V]; the multi-graviton no-go [8†]; a signature obstruction; an explicit tuning test [V]”, and #11 §15 does not name them. #11 governs the count. → assessment.
  • When “theory” becomes the word. Calc note #6 §5: “Pass ⇒ the geometric core stands and ’theory’ becomes the defensible word”; #9 §11: “The word ’theory’ awaits items 1–2 of §10”; #11 §15: it “still waits on items 1–3 above”. #11 governs. → Born’s answer.
  • How far Debt 1 is resolved. The lab notebook’s v0.6 addendum is headed “Debt 1 closed” and #9 §5 “(Debt 1: paid)”; calc note #8 says “Debt 1: structurally paid”, the handoff “closes Debt 1 (structural)”, and #11 heads §7 “(Debt 1)” with the residue open. → the three debts.
  • Safety of ordinary matter. #5 §E and #6 §4 combine X’s short range with a weak coupling through ordinary matter’s dual stress (“suppressed” in #5, “unenhanced” in #6); #7 §4 requires “the massless combination to dominate SM couplings” (SM: Standard Model); #8 §3 rests safety on range alone, with couplings of gravitational strength (“by range, not decoupling”), which #11 §7.5 keeps as “Yukawa-cut at 1/M_X”. #8 and #11 govern. → safety by range; constrained bimetric gravity; Yukawa forces.
  • The graviton-mass bound. #7 §4 logs graviton-mass bounds from gravitational waves, “m_g ≲ 10⁻²³ eV territory”, as a check “for the mixing angle”; #8 §3 says they “apply to the even eigenstate, which is exactly massless”, and #11 §7.5 and row 6 state them as satisfied identically. → spectrum and parity; row 6.
  • “Yukawa-cut in momentum”. #13 says X “modifies the dual cone only at short range in momentum [D — §7 of the checkpoint]” (§1) and that “dual-geometric effects are Yukawa-cut in momentum [D — checkpoint §7]” (§6); the handoff’s chat-only list has “dual Newtonian limit = Yukawa in momentum = the gate” (HANDOFF.md §4). The section cited says “Yukawa-cut at 1/M_X”, of the couplings of ordinary matter (#11 §7.5), a range in position. #11 governs, and the reading in momentum stays chat-only (review/wiki-build-flags.md item 29). → two gravitational charges and the conjugate field equations; safety by range; the equivalence principle as dual relativity.
  • The second metric. #1 §4’s “Ghost accounting” says “There is no second independent metric”; the v0.4 addendum and calc note #6 make X a second graviton. Superseded. → why X must be massive; the geometric action (superseded); the notebook’s argument against a ghost.

Dark matter#

  • Cliff to knee. #1’s exponential cliff (v* ≈ 120 km/s; killed by “Robust nonzero self-interaction at v > 3v*”) became #9’s and #11’s knee (“Knee at v* ~ 10² km/s”; killed by “Robust self-interaction at v ≫ v*”), with the tail shape open (#11 §8, §13). → the gated scattering law; row 1.
  • The wave-island suppression. Calc note 3a has “(v*/σ)³”; 3b, 3c and #11 have (v*/σ)⁴. → row 3; the gated condensation rate.
  • The wave island’s upper edge. 3a’s consequences give “m_χ ≲ meV”, its corollary and 3b’s setup 0.1 meV; 3c, final for the Debt-3 scope, and the notebook’s v0.2 addendum write 10⁻⁴ eV. → the Debt-3 calc notes; the wave island.
  • Row numbers. In #1 §9 and the Debt-3 notes, rows 3 and 4 are velocity granularity and Fornax friction; in #9 and #11 they are the island discriminant and dark energy. The wiki uses #11’s numbering and calls the withdrawn rows “old row 3” and “old row 4”. → history of the predictions table.
  • Open problem 5 and the relic abundance. The lab notebook’s v0.2 addendum says “open problems 3 and 5 close (5 via misalignment production on the wave island)”, 3b that “Open problem #5 (cannibalism-safe relic abundance) is moot on the wave island”, and #9 that misalignment closes “a separate open problem”. These use #1 §11’s numbering; item 5 of #11 §14 is the dual-stress enhancement. #11 §9 states the closure for the wave island only, and §12 keeps the 5.4 : 1 ratio open for both candidates; #11 governs. → relic abundance by misalignment on the wave island; Open: polarization-genesis.
  • Symbols #11 does not define. #11 §8 writes M(k,q) = 4πα̃m_χ/(q² + m_φ²)·F(k²/μ²) without defining α̃, m_φ or F. The wiki takes them from #1 §3 and #9 §6, the documents #11 superseded. → the velocity gate.
  • The dark-matter candidates. #10, #12, HANDOFF.md §2 and #11 v2.0 give three candidates; #11 v2.1 gives two, χ particles and the X-condensate. → dark-sector candidates; row 11.

Dark energy#

  • The reading of DESI. Data from the Dark Energy Spectroscopic Instrument (DESI) were read as support in #1 §7 (“the sign pattern DESI reports”), #9 §8 (“exactly the drift this sector requires”), HANDOFF.md §2 (“Consistent with DESI DR1/DR2 drift hints”, DR1 and DR2 being Data Release 1 and Data Release 2), #10 (“exactly the required weakening”) and #12 (“the required behavior”). The root CLAUDE.md, #11 §10’s paragraph “Under pressure (v2.1)” and round-3 ruling 11 record DR2’s phantom crossing above z ≈ 0.4: the sector is under real pressure. #11 §10’s own italic passage still says “DESI’s hints of weakening dark energy are exactly the required drift”; that inconsistency inside #11 is unreconciled in its text, and the wiki takes the status from rank 1 and the technical paragraph. → DESI DR2’s phantom crossing.
  • What a constant w = −1 would kill. #11 row 4: “DR3+ constant −1 (kills τ-sector); robust intrinsic w < −1 (kills outright)”, DR3 being Data Release 3; HANDOFF.md §2 and #10 (“Constant kills the theory’s heart”) agree. #12 says “constant is impossible” and that the framework “survives only the first outcome”, a continued weakening; #14’s exclusion condition 6 has both robust outcomes kill “the parent framework’s cosmological sector”. #11 governs. → row 4.
  • What a phantom w would kill. #1 §7 item 1 says a robust intrinsic w < −1 “falsifies this sector outright”, and #14’s exclusion condition 6 confines the kill to “the parent framework’s cosmological sector”; #1 §9 row 5, #9 §9 row 4 and #11 row 4 write “kills outright”, and HANDOFF.md §2 “kills the framework outright”. #11 governs; no document says why the kill reaches beyond the sector. → how much a violation kills; row 4.
  • Why the dictionary changed. #9 credits “the Lagrange-multiplier bookkeeping”, #11 “the constraint’s Jacobian” and #1 the constraint’s “volume Jacobian”; the result, w_eff = −w̃, is the same, and the wiki uses #11’s wording. → the duality dictionary.
  • The potential’s origin. #1 §3 derives the existence of τ’s potential from “the explicit breaking of Grassmannian rotations by the rigid ω (P2)”; calc note #5 §F reopens the origin under P2′, and #11 v2.2 states that a definite polarization needs a ρ-preserving potential whose derivation is open. → τ: hilltop quintessence; Open: the origin of the ρ-preserving potential.
  • The definition of τ. #1 §2 writes τ ≡ f · arg det²(·); calc note #5 §C calls τ “arg det of the boundary variable”, with no square and no scale f; #11 §6 calls it “the Maslov phase of the boundary variable”. Neither earlier document says which object its argument stands for, and neither compares the two forms. #11’s wording is the current statement; the wiki’s reading, that both name the same angle up to the scale f, is on the page that holds the topic. → τ as the Maslov phase.

Postulates and the toy models#

  • The breaking pattern. #1 §2: “The breaking pattern is ℤ₄ → ℤ₂”, a discrete choice; #11 v2.2’s P2′: “ρ sits inside a continuous U(1), and the polarization is a Goldstone angle rather than a discrete choice [D][V]”. → the order parameter; the polarization as a Goldstone angle.
  • Exact or gauged charge conjugation. #11’s P4 says gravity-induced mixing “vanishes if hidden charge conjugation is exact”; round-3 Decision 1 says “zero if hidden charge conjugation is a gauged symmetry”, and the v3 worklog explains why the difference matters: “Quantum gravity forbids an exact global C … a gauged C (O(2)/O(3)-type) remains a loophole” (item R4). #11 outranks the adjudication, so its wording is the current statement. → P4; row 7.
  • The earlier kinetic-mixing bound. Round 1 led #14 v2 to add a postulate with “ε ≲ 10⁻⁵ exclusion” (HANDOFF.md §6); #11’s strict P4 has the gravity-only ε ≲ 10⁻¹³. The two belong to different documents and contexts, and #11 governs for the program. → kinetic mixing between sectors.
  • The naive potential. The worklog’s S4 pass used −μ[Tr(K K_ref)]², which round 4 found unbounded below once H is dynamical (findings F1 and F2); the note v2 uses the bounded V_b. → Obituary: the naive ρ-preserving potential; the bounded potential V_b.
  • V_b’s zero mode (C28). The round-4 adjudication calls it “the residual diagonal squeeze, which is an exact symmetry” (F2) and asks for a “local minimum up to the exact residual squeeze” (revision 1); the note v2 says “It is not symmetry-protected, because V_b breaks the squeeze away from K = ±K_ref” (§4). The note (rank 2) outranks the adjudication (rank 3), and review/wiki-build-checks/squeeze_check.py finds V_b not squeeze-invariant off K = K_ref (review/wiki-build-flags.md item 12). → the bounded potential V_b; Goldstone modes and the Higgs mechanism.
  • “Ising class”. The worklog calls the Monte Carlo phase “Ising class” and the note v1 “Ising-class”; the adjudication’s revision 1 asks for “ordered Z₂ phase”, and #11 §14 item 11 says “an ordered ℤ₂ phase in 1+1 in the frozen-H reduction”, as the note v2 does. → Monte Carlo: an ordered ℤ₂ phase.
  • The Monte Carlo control values. The note v1 quoted “0.078 → 0.033 → 0.014” from fixed seeds; the adjudicator’s long runs give 0.0653, 0.0325 and 0.0164; the note v2 gives four-seed means 0.0653 ± 0.0043, 0.0338 ± 0.0013 and 0.0155 ± 0.0004, which the gate reproduces. The adjudicator’s and v2’s values at L = 32 and 64 are not reconciled; the wiki cites v2’s, the higher-ranked. → Monte Carlo.
  • Two Hessian normalizations. In the real Grosse–Wulkenhaar model the referee and the adjudicator printed the lowest Hessian eigenvalues at the two vacua, and the adjudicator notes that “the referee’s normalization is half of mine” (F4). The lists are not reconciled mode by mode; the wiki quotes only the free-energy difference, 2.634, on which both agree. → Open: the real model’s one-loop preference.

The withdrawn soliton manuscript#

These concern #14 and its review record. The manuscript is withdrawn, so each is settled by the adjudication and the gate, and most are moot.

  • The gravitational-wave band. #14 §4 gave “~1e5 to 1e7 Hz”; the referee evaluated it with the visible temperature at the transition set to the hidden symmetry-breaking scale and found “1.35e5 - 2.47e7 Hz”, “CONFIRMED”; ruling 5 carried the corrected temperature ratio ξ into the band and moved its upper end to 3.2×10⁷ Hz, which verify/soliton_obituary.py reproduces with the visible temperature at which the colder hidden plasma reaches that scale (printing 3.17e+07). The record follows the adjudication and the gate. → the hidden sector’s thermal history.
  • The ψ relic window. The referee’s Boltzmann integration gives “28–46 / 96–153 GeV” for 10% and all of the dark matter; the adjudicator’s recount gives “45–49 GeV” and “146–158 GeV”: “We agree to within ×1.6, and v3’s 0.1–0.3 TeV was wrong” (ruling 4). The record carries the adjudicator’s numbers, which the gate checks. → Obituary: the ψ relic window.
  • The W′ overclosure at two stages. The v3 worklog (item O1) had m_W′ = “1.2–2.2×10¹¹ GeV” and a relic of “0.8–15×10¹⁶ × the observed density”; #14 v3 and #11 §12 give an overclosure “by 10¹⁶–10¹⁷”, at v3’s benchmark. The stage numbers were never reconciled with #14’s; the record cites #11, the adjudication and the gate. → W′ overclosure.
  • The dimension-five mixing estimate. The worklog (item R4) planned “ε ~ ⟨Φ⟩/M (≈ 10⁻⁸–10⁻⁷)”; #14 v3 printed “epsilon ~ 1e-7 to 1e-6”. The two come from different stages of the benchmark and were never reconciled; both are moot. → Obituary: Planck-suppressed adjoint mixing.
  • The count of monopoles inside #14. The referee found #14’s gravitational-wave paragraph, which “contemplates a first-order transition with f*/H* = 1-100”, “flatly inconsistent with ‘p = 1 as the upper end’ of Sec. 3”, since bubble counting gives far more monopoles (audit notes, Step 4(a)). It died with the manuscript. → Obituary: the Kibble normalization.
  • Ruling 3’s range. The adjudication attributes “1e9–1e12 overproduction” to the referee’s Kibble–Zurek integration, which the referee’s notes give as 1.1e12–2.2e12, the lower end coming from an analytic estimate; the verdict is unaffected (review/wiki-build-flags.md item 21). → round-3 rulings.

Pointers inside the lab notebook#

  • Section pointers in #1 (C21). Its P2 points to “§5” for the potential, which is in §3, and to “§7” for the cosmological constraint, which is derived in §6; §4 also cites “§7” for the constraint (review/wiki-build-flags.md items 10 and 25). The wiki cites the notebook by heading. → the geometric action and the v0.1 action; Original P2.

Sources#

  • wiki/CLAUDE.md ‘The wiki is derivative’ — the order of precedence and the dead-stays-dead rule
  • CLAUDE.md ‘Since the handoff’ and ‘Layout’ — the top-ranked rulings and the instruction on arbitration scripts
  • papers/broken-born-checkpoint-v2.md and papers/reciprocity-toy-models.md — the rank-2 statements, including the inconsistencies inside #11
  • review/round4-adjudication.md and review/round3-adjudication.md — rulings, decisions and revisions; review/round3/referee/audit-notes.md and review/round4/referee/audit-notes.md — the referees’ readings
  • papers/conjugate-special-relativity.md §1, §4, §6 and review/v3-worklog.md (items O1, O3, R4) — the two dual cones, the dark-sector kinematics and the worklog’s stage numbers
  • HANDOFF.md §1, §2, §4, §5, §6 — the superseded state of 2026-10-19
  • notes/broken-born-theory.md, notes/broken-born-program-v1.md, the calc notes #2–#8, notes/toy-lagrangian.md and notes/knot-dark-matter-standalone.md — the earlier statements
  • popsci/angle-of-the-mirror.md, popsci/universes-other-half.md — the popular framing
  • verify/battery.py, verify/toy_gw.py, verify/soliton_obituary.py and scripts/check.sh — what the gate does and does not check
  • review/wiki-build-flags.md and review/wiki-build-checks/README.md — the separate list of suspected errors, with its executed checks and inventory numbers
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