The checkpoint: #9 to #11 v2.2
The checkpoint is the program’s paper-length statement of everything it has derived, predicted, retracted and left open, with every claim tagged by where it came from. Its first version, #9 (“The Broken-Born Program” v1.0), consolidated the lab notebook and the calc notes into one document with a plain-language passage opening every section. Its successor, #11, is the current reference for the full program. Version 2.0 added a methodological preface with a machine-verification battery, sections on charge lattices and on the dark-sector candidates, a reference list and an audit of the founding ideas; version 2.1 recorded the outcome of review round 3, retiring the soliton candidate and putting the dark-energy prediction under pressure; version 2.2 recorded the toy-model results. #11 is a working checkpoint, not to be submitted until its citations from memory have been checked against their sources.
Status: Record — #11 v2.2 is rank 2 in the wiki’s precedence order and “the current reference for the full program” (root CLAUDE.md); #9 is superseded by #11 and kept as the audit trail (HANDOFF.md §3: “v1.0 — superseded by #11”; #11 header: “Supersedes v2.1, v2.0 and v1.0”). #11’s versions are in git log -- papers/broken-born-checkpoint-v2.md: v2.0 as imported (8d588f6, 2026-10-19), v2.1 (e1c1f67, 2026-10-19) and v2.2 (6ee74d0 and 6606734, 2026-10-19 and 20).
What the checkpoint is#
#11 is titled “The Broken-Born Program: A Working Checkpoint” and states its form in the header: “Every section opens with a plain-language passage (italic), followed by the technical record.” Every claim carries a provenance tag, [D] derived in the program, [T] established literature, [P] postulate, [O] open or [V] machine-verified, and every reference a mark, [S] for “retrieved by live search during this project” or † for “cited from model memory — verify against the source before external use” (provenance tags and citation marks). Its footer gives the attribution, “conjecture and direction, P. R.; derivations, counterexamples, verification battery, and drafting, Claude (Anthropic)”, and the condition on its use: “Working checkpoint — not for submission until the † audit (open item 10) completes” (Open: the † literature battery; the collaboration).
The wiki takes its top-level structure from #11: “The top level follows the program’s argument as #11 builds it” (wiki/CLAUDE.md). Most pages cite #11 first, and where #11 and an older document differ, #11 governs, unless the root CLAUDE.md says otherwise (conflicts between sources).
#9: “The Broken-Born Program”, v1.0#
The header: “Version 1.0 — consolidation of the full development arc. Each section opens with a plain-language passage, then the technical record. Provenance tags: [D] derived here, [T] established literature, [P] postulate, [O] open.” #9 is undated; it follows the Debt-1 notes and precedes the first popular article in HANDOFF.md §3’s creation order, and the handoff describes it as the “First paper-shaped consolidation; lay passage opening every section; tag system [D]/[T]/[P]/[O]”. It was imported with the other files on 2026-10-19 and placed in notes/ as superseded (commit 008c3ee).
Its sections are §0 “Two abstracts”, §1 “The question”, §2 “Postulates — including the one the mathematics rejected”, §3 the kinematic core and the compatibility theorem, §4 the modular field, §5 “The second graviton and its mass (Debt 1: paid)”, §6 “Conjugate matter and the gate (Debt 2: mechanism paid)”, §7 “The death of momentum clumping (Debt 3: closed, negative)”, §8 cosmology, §9 predictions and kill conditions, §10 open problems and §11 “Assessment” (the three debts). It cites literature without a reference list and asks that “All citations flagged [T — verify] should be checked against sources before any submission.” Its provenance note reads “developed in dialogue; conjecture and direction by P. R.; derivations, counterexamples, and drafting by Claude (Anthropic)”, without the verification battery that #11 adds.
Its assessment counted “at least two results that stand on their own regardless of its fate”, the symplectic partner of the graviton and “the palindrome theorem cancelling the symmetric-bimetric vacuum energy”, and said that “The word ’theory’ awaits items 1–2 of §10”. #11 revised both (Assessment).
#11 v2.0: what it added#
#11 v2.0 arrived in the repository with the import of 2026-10-19 (commit 8d588f6), subtitled “Spontaneously broken reciprocity, a massive momentum-space graviton, polarized charge lattices, and the dark-sector trilemma”. The handoff lists what it added to v1.0: “Supersedes #1 and #9. Adds: methodological preface + 7-test machine-verification battery; charge-lattice §11; dark-sector trilemma §12; 25 references flagged † (memory — verify) vs [S] (live-searched); PM/Hossenfelder novelty downgrade; Appendix A supposition audit (11 items with fates)” (HANDOFF.md §3), PM being partially massless. In the wiki:
- the preface is §2, with Tier 1 checked by the verification battery and the tiers on claim tiers and selection bias;
- §11 is the symplectic charge lattice and the rest of electric–magnetic duality;
- the trilemma offered three dark-matter candidates, χ particles, an X-condensate and “Conjugate knots”, topological solitons of a p-local gauge sector (dark-sector candidates);
- the reference list ran [1]–[25] (References);
- the novelty downgrade is §7.4, “Literature position (updated by this session’s search — honesty upgrade)” (Open: the partially-massless comparison);
- the audit is Appendix A (founding suppositions and their fates).
In v2.0 the compatibility theorem was tagged “[D][V]”, as derived in the program, and §9’s plain-language passage promised “in §12, one loophole for individual knots”. The predictions table gained row 11 (history of the predictions table).
v2.1: after round 3#
v2.1 was committed on 2026-10-19 at 17:29 (e1c1f67), the same afternoon as the round-3 decisions (round-3 decisions and lessons). The current header lists its changes: “the soliton candidate is retired (§12); the compatibility theorem is re-attributed to the Born-geometry literature (§5); P4 is taken strictly (§4); §10 records DESI DR2’s phantom crossing”, DESI DR2 being Data Release 2 of the Dark Energy Spectroscopic Instrument. The footer adds: “v2.1 amendments: decisions delegated by P. R. to Claude; record in review/round3-adjudication.md.”
The changes in detail:
- Title and abstracts. “the dark-sector trilemma” became “the dark-sector question”. The plain abstract now ends that the topological candidate “was worked out, failed its own abundance arithmetic, and is retired, leaving particles or a condensate”.
- §2. A caution: “a verification script confirms arithmetic, not the model it encodes — the §12 failure passed a script whose physics input was wrong, and was caught only by an independent review” (verification checks arithmetic, not the model).
- §4. P2′ notes that “That η should be dynamical rather than fixed was argued independently in metastring theory [26S]”. P4 is “taken strictly since v2.1: no kinetic mixing between the sectors beyond what gravity induces, … ε ≲ 10⁻¹³ [27S]” (P4).
- §5. The compatibility theorem becomes [T][V]: “It is the Born-geometry compatibility statement of Freidel, Leigh and Minic … The block proof and the machine check are this program’s.” The plain passage was rewritten to match (the compatibility theorem).
- §10. The paragraph “Under pressure (v2.1):” records DESI DR2’s own statement of “a phantom crossing to w < −1 above redshifts z ≃ 0.4”, and concludes: “The framework’s strict w ≥ −1 therefore stands against the direct reading of the data” (DESI DR2’s phantom crossing).
- §11.1 and §12. The candidacy of conjugate monopoles “as the dark matter itself is retired”, and the trilemma becomes “two candidates, and the obituary of a third”, with the obituary in the form what was claimed, how it was tested, why it failed, what survives (Obituary: superheavy conjugate solitons). Its [V] numbers are gated in
verify/soliton_obituary.py(the soliton-obituary script). - §13–§15 and Appendix A. Rows 3, 4, 7 and 11 and the withdrawn list change; §14 items 8 and 9 lose the soliton items; §15 adds the obituary, the re-attribution and DR2 to the degeneration risks; Appendix A items 3–5 record the retirement.
- References. “[21] upgraded to [S]; [26]-[29] added, all INSPIRE-checked” (commit e1c1f67).
v2.2: the toy-model results#
v2.2 came in two commits. On 2026-10-19 at 22:29 (6ee74d0), §3 gained an attribution marked “(v2.2)”, while the header still read 2.1: “the idea that a preferred polarization breaks Born duality is Freidel, Leigh and Minic’s”, with the program’s addition stated as reading it “as spontaneous breaking, with η as the order parameter” (broken Born duality). The commit message: “Toy-derived amendments to secs. 10 and 14 wait for the round-4 review.”
On 2026-10-20 at 18:54 (6606734), after the round-4 adjudication, the header became “Version 2.2 (checkpoint), amended 2026-10-20”, with the change list “§3 credits Freidel–Leigh–Minic for ‘broken Born duality’; P2′ (§4), §10 and §14 item 11 record the toy-model results.” The three toy-model additions:
- P2′’s refinement: “with only ω rigid, ρ sits inside a continuous U(1), and the polarization is a Goldstone angle rather than a discrete choice [D][V]”, with the consequences that a definite polarization needs a ρ-preserving potential and that breaking ρ is physical only once matter couples to the sign of K (the polarization as a Goldstone angle; the twisted element).
- §10’s “Toy-model support (v2.2) [D][V]”, which ends: “None of this tests the cosmology; it only shows the structure is consistent.”
- §14 item 11, the toy Lagrangian, “Met in the referees’ wording by the coset model of (H, K) with a bounded ρ-preserving potential”, with three open ends (acceptance criterion 1).
The same commit made the toy-model note v2 and applied the round-4 revisions (review round 4), except the comparison with an exactly solved model that revision 4 asked for, which v2 says it has not carried out (flag 42 in review/wiki-build-flags.md). The root CLAUDE.md bullet “#11 is now v2.1” was not updated (CLAUDE.md and the README; flag 38 in review/wiki-build-flags.md).
#11 v2.2, section by section#
| Section | What it holds | Where the wiki covers it |
|---|---|---|
| §1 | two abstracts | the research program |
| §2 | the methodological preface: tiers, the battery, the caution | claim tiers; the battery |
| §3 | the question, mandatory breaking, the attribution to Freidel–Leigh–Minic | Born’s question; mandatory breaking; broken Born duality |
| §4 | postulates P1, P2′, P3, P4, P5 | postulates P1–P5 |
| §5 | the split-quaternion algebra, the compatibility theorem, the nontriviality theorem | Born geometry; the nontriviality theorem |
| §6 | the modular field Z = X + iY | the modular field |
| §7 | the massive momentum graviton: the chain, the tuning test, the palindrome, the literature position, the spectrum, Born’s answer | the momentum graviton X; the tuning test; the palindromic branch |
| §8 | conjugate matter and the gate | conjugate matter and the velocity gate |
| §9 | the obituary of momentum clumping | momentum clumping (Debt 3) |
| §10 | cosmology: the constraint, the dictionary, dark energy, the pressure from DR2, the toy-model support | cosmology: scale-factor duality; dark energy |
| §11 | polarized charge lattices | electric–magnetic duality |
| §12 | the two candidates and the soliton obituary | dark-sector candidates, in dark matter |
| §13 | predictions and kill conditions, rows 1–11 | predictions and kill conditions |
| §14 | open problems 1–11 | open problems and the queue |
| §15 | the assessment | assessment |
| App. A | the founding suppositions and their fates | founding suppositions |
| References | [1]–[29], marked † or [S] | references |
#9’s sections map onto #11’s as §0 → §1, §1 → §3, §2 → §4, §3 → §5, §4 → §6, §5 → §7, §6 → §8, §7 → §9, §8 → §10, §9 → §13, §10 → §14 and §11 → §15. #11’s §2, §7.4, §11, §12, Appendix A and reference list have no counterpart in #9.
Inconsistencies inside #11#
Some statements in #11 disagree with others in the same document or overstate what the gate checks. The wiki records each where it arises and lists them on conflicts between sources:
- §10’s plain passage and its technical paragraph. The italic passage still ends “The sky is voting now: DESI’s hints of weakening dark energy are exactly the required drift”, a sentence that stood in v2.0; the “Under pressure (v2.1)” paragraph below it reads the data the other way. The wiki follows the paragraph and the root
CLAUDE.md. - The loophole. §12 says the Debt-3 loophole “remains untested, but has no candidate”; §14 item 8 says “The soliton-spectrum and p-localization items are closed by the §12 obituary” (Open: the topological loophole).
- “The empty set” or “measure zero”. §11.1 and Appendix A item 5 word P.R.’s correction differently (conjugate monopoles as ontology).
- J or K. P2′ calls J “the real structure”; §14 item 11 makes η = ωK the order parameter (the order parameter).
- What the machine checks. §2’s “det H = 1 across the whole family” rests on a test of one random member, and §7.2’s “provably outside the linear-in-eₙ span (T7)” on a numerical test of p₄ alone; §7.2’s “the 66.58-vs-63.72 test of §2” points to a section that does not print the figures, which are in
HANDOFF.md§5 and the battery’s output (flag 36 inreview/wiki-build-flags.md). The wiki tags the family-wide and nonlinear statements [D] (the verification battery). - Undefined symbols. §8 uses α̃, m_φ and F without defining them; the wiki takes them from #1 §3 and #9 §6 (the velocity gate).
What the wiki flags#
review/wiki-build-flags.md lists suspected errors in #11 or #9, quoted on the wiki’s pages as written: item 1, the “discrete” polarizations of §5 (and #9 §3); item 5, “M_X ∝ 2(β₁+β₂)” in §7.5 (and #9 §5 item 6), where the source note has the squared mass (spectrum, parameters and reciprocity parity); item 6, §7.3’s “by symmetry”; item 7, “The unique consistent structure” in §7.1; item 9, reference [24][S], which has no authors; item 20, reference [23]†, whose title and arXiv number belong to different papers; item 23, the identification of a·ã = 1 with the |Z| = 1 locus in §6 and §10; item 27, the sign of τ’s potential V = V₀[1 + cos(τ/f)] in §10 (and #9 §8), against the turnaround it needs (Open: the sign of V(τ)); item 28, the formula 4π/e² beside the magnetic coupling ≈ 34 in §11.2; item 36, §7.2’s pointer to §2 for the figures 66.58 and 63.72; item 39, §7.5’s reciprocity parities, which hold for reciprocity as §7.3’s frame exchange and not under §6’s Z → −Z⁻¹ (two actions of reciprocity); and item 43, §10’s thawing corridor (and #9 §8), which lies in the region of the w₀–wₐ plane where DESI DR2’s fits lie, a relation §10 does not state although it gives the corridor and DR2’s crossing in one paragraph (the corridor and DR2’s crossing). The flags’ audit (2026-10-22) confirmed all of these except item 39, which depends on which action of reciprocity is meant. Item 32 is a lead, not a source error: the status of CMB-S4, the cosmic microwave background experiment row 10 names as a probe, is unchecked and belongs to the † battery. Item 38 concerns the root CLAUDE.md’s statement of #11’s version (above).
What the wiki does not copy#
Some of #11’s plain-language passages use phrasing the wiki’s register excludes (wiki/CLAUDE.md, ‘Voice’): physics that “plays favorites” (§1), a field that “wants” to be a second copy of gravity and “nature forbids identical twins of the graviton” (§7), and “one state, two ledgers” and “one event, two ledgers” (Appendix A items 2 and 7), with “the conjugate ledger” in §10. The wiki states the same content without attributing intentions to fields or nature, and writes “two descriptions” for the two ledgers (the conjugate universe).
Sources#
papers/broken-born-checkpoint-v2.mdheader — the version line and the v2.1 and v2.2 change lists; §1–§15, Appendix A and References — the sections in the table; footer — the provenance line and the submission condition. Its earlier versions are in the repository’s history: commit 8d588f6 (v2.0 as imported), e1c1f67 (v2.1), 6ee74d0 and 6606734 (v2.2), with their commit messages.notes/broken-born-program-v1.md— #9’s header, sections, assessment and provenance noteHANDOFF.md§3 rows 9 and 11 — v1.0’s standing and what v2.0 addedCLAUDE.md‘Layout’ — #11 as “the current reference for the full program” and #9 “superseded by #11”; ‘Since the handoff’ — the v2.1 changesreview/round3-adjudication.md‘Decisions’ — the decisions v2.1 records;review/round4-adjudication.md‘Revisions for v2 of the note’ — the round behind v2.2verify/battery.py— the Tier-1 checks of §2review/wiki-build-flags.mditems 1, 5, 6, 7, 9, 20, 23, 27, 28, 36, 39 and 43 — suspected errors in #11 and #9, with their audit verdicts; item 32 — a lead on row 10; item 38 — the rootCLAUDE.md’s stale version of #11; item 42 — the round-4 revision that v2 did not carry out