Superseded statements

This register lists the statements the program once made and later replaced with corrected versions. A superseded statement differs from a dead claim: the subject survives, but its earlier form is no longer the program’s position, often because a calculation or a review forced a repair. Each line names the old statement, what replaced it and where the replacement is recorded. The older documents are kept as an audit trail and still contain the old forms: the lab notebook, for example, keeps its version-0.1 body with the corrections appended as addenda, so the old forms read there as if they were current.

Status: Record, a register current to 2026-10-21 — no tags of its own; each replacement keeps the tag its source gives — the replacements are recorded in higher-precedence sources: checkpoint #11 v2.2, the toy-model note v2, the review adjudications and the root CLAUDE.md.

Two pages have the status superseded. Every other entry is an earlier form recorded on the page of the claim that replaced it, under a heading “Superseded: …” that this register links; the few recorded in a page’s body without such a heading are marked “in the body”. The documents themselves succeed one another: the lab notebook #1 (version 0.1 with addenda v0.2–v0.6), then the program v1.0 (#9), then checkpoint #11, whose v2.2 “Supersedes v2.1, v2.0 and v1.0”. The notes are “superseded as reference but kept” (root CLAUDE.md).

Superseded is not dead. The heuristic w_eff = −2 − w̃ was superseded by w_eff = −w̃, and the claim that rested on it, that conjugate collapse powers our expansion, died (Obituary: conjugate collapse powers our expansion). The naive toy potential, by contrast, was replaced by a bounded one but is recorded as dead in the graveyard.

Superseded pages#

  • Original P2: both structures rigid (superseded) — the lab notebook’s second axiom made both the symplectic form ω and the neutral metric η non-dynamical, leaving the degrees of freedom to H alone (#1 §1) → P2′: only the symplectic form is rigid, with η emergent as the order parameter (#11 §4; #1 addendum v0.3). #11 calls the correction forced: by the nontriviality theorem the theory has content beyond general relativity plus self-interacting dark matter if and only if η is emergent. Of the “triple duty” #1 §1 gave P2, the second graviton it was to remove returned as the massive X, the cosmological constraint a·ã = 1 survives from the rigidity of ω alone (#11 §10), and the origin of the dark-energy potential became an open problem; the first and the last are listed below.
  • The geometric action S_H and the v0.1 action (superseded) — the notebook’s complete action S = S_H + S_τ + S_x + S_p + S_mix, its Einstein-like S_H written with ω and η frozen (#1 §3), and the argument that no second independent metric, and so no ghost, can arise (#1 §4) → P2′ unfroze η, X was found to be a second graviton (#1 addendum v0.4), and ghost freedom now comes from the frame tier (#11 §7.2). #11 writes no full action; deriving the wedge sector from S_H is OP1.

Superseded statements by section#

The research program#

  • Superseded: the v0.1 arena with three structures — the notebook’s P1 put three structures on phase space, ω, η and H (#1 §1) → #9 §2 and #11 §4 list only ω and H; η survives as a property of the vacuum.
  • Superseded: the v1 assessment — #9 §11 counted “at least two results that stand on their own regardless of its fate”, one sharpening of the hard core and two degeneration risks → #11 §15 counts one standing observation and “one identity awaiting a novelty verdict”, two sharpenings, and adds to the risks three demotions and the second data release of the Dark Energy Spectroscopic Instrument (DESI).

Phase-space geometry#

  • Superseded: the three-way classification of X — calc note #5 §D posed the nature of the momentum graviton X as a computation with three outcomes, healthy, auxiliary or ghost → calc note #6 answered in other terms, “massive spin-2, conditionally healthy”, with the shift symmetry removing the auxiliary outcome; the curvature expansion itself is reported in no document. The same history from the side of the forcing chain is listed under gravity.
  • The compatibility theorem as “derived here” (in the body of the compatibility theorem) — tagged “[D — rigorous]” in calc note #5 and presented as derived in #11 v2.0 → since #11 v2.1 the statement is Freidel, Leigh and Minic’s [T], and the block proof and its machine check [V] are the program’s (#11 §5).

Spontaneous breaking of reciprocity#

  • Superseded: the discrete breaking pattern — ℤ₄ → ℤ₂ = {1, ρ²}, with J = η⁻¹H as the order parameter [D] (#1 §2) → “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]” (#11 §4). Prediction row 9 still calls the absent linear term in photon dispersion “ρ²-protected”, an argument written out only in #1 §4.
  • Superseded: the rigid symplectic form as the source of the tilt — the notebook’s account of the dark-energy potential: its “existence comes from the explicit breaking of Grassmannian rotations by the rigid ω (P2)” (#1 §3) → under P2′, ω alone leaves the polarization a Goldstone angle, a definite polarization needs “more structure than ω alone” (#11 §4), and where that structure comes from is open. The same statement is recorded on τ’s page, listed under cosmology.
  • Superseded: a coupling built from K alone — the worklog’s “The ρ-covariant interaction I_K[W]” and the reviewed note’s “K-covariant” coupling → round-4 finding F5 showed that it needs H as well, and v2 calls it “A coupling built from (H, K)”, covariant under the SO(2) fixing H = 1 (note §5). verify/toy_s5.py still says “built from K” (flag 10 in review/wiki-build-flags.md).
  • Superseded: every derivation selects the pair — the worklog’s literature summary and the reviewed note’s agreement with the double-field-theory literature, “where every derivation selects the pair” of null sections → restricted to d = 1 by the round-4 ruling and revision 5; for d > 1 the section condition leaves “a continuous family of sections” (note v2 §5).
  • Superseded: the worklog’s first verdict — acceptance criterion 1 “Met, in the referees’ wording, by the coset toy plus a τ-type potential”, the breaking “(Ising class in 1+1, Monte Carlo verified)” → met “by the coset model of (H, K) with a bounded ρ-preserving potential”, with “an ordered ℤ₂ phase in 1+1 in the frozen-H reduction” (#11 §14 item 11). The τ-type potential is unbounded below with H dynamical (Obituary: the naive ρ-preserving potential).
  • Superseded: Ising-class breaking in model I — the note’s first version claimed Ising-class breaking of ρ in model I in 1+1 → round 4 narrowed the claim from model I to the frozen-H reduction, since the simulation never let H move, and from a universality class to order: “ordered Z₂ phase”, not “Ising class” (revision 1; note v2 §4).
  • Superseded: the first version’s control values — the high-temperature control “0.078 → 0.033 → 0.014”, from fixed seeds and without error bars → the four-seed means 0.0653 ± 0.0043, 0.0338 ± 0.0013 and 0.0155 ± 0.0004 (note v2 §4). The round-4 ruling: “Fixed seeds gave reproducibility, not accuracy; the numbers lacked error bars.”
  • Superseded: the first version’s unrestricted theorem — the note’s first version applied the two-dimensional no-breaking theorem to all of model I’s continuous breaking, ignoring the exception for its non-amenable Sp(2,ℝ) → restricted to the compact SO(2) that contains ρ (round-4 ruling; note v2 §4); whether the coupled model breaks that SO(2) is open.
  • Superseded: the reversed sign of the polarization — the worklog’s first version of a line in its chunk 2 had the sign of the polarization reversed → corrected on 2026-10-19 to “β = 0 is broader in x than in p (Δ(0) = +10.88 > 0)”, a sign the round-4 referee confirmed independently.
  • Superseded: “Increasing the truncation adds only massive levels” — the note’s first argument for restoration in the complex model → v2 rests it on the exact independence of the condensate phases and adds the caveat that the bare μ² is renormalized and that fixed bare μ² “is not a consistent large-N limit” (round-4 finding F6, accepted, not re-checked). The tadpole’s coefficient, ln N or 2 ln N, is flag 11.

Gravity#

  • Superseded: no second graviton under the original P2 — #1 §4: “There is no second independent metric” → reversed by the v0.4 addendum once calc note #6 showed X to be a second graviton; ghost freedom now comes from the frame tier, “ghost-free by construction” (#11 §7.2).
  • Superseded: the three-way classification of X — X as healthy, auxiliary or ghost, “the single most important remaining calculation” of calc note #5 §D → calc note #6 §5: “Not healthy-by-default, not auxiliary, not necessarily ghost: massive spin-2, conditionally healthy”; whether X carries a ghost became the condition that the tuning test examined.
  • Superseded: earlier forms of the safety argument — calc notes #5 and #6 combined X’s short range with a weak coupling of ordinary matter to X through its dual stress, and calc note #7 required the massless combination to dominate the couplings of ordinary matter → calc note #8 §3: safety by range alone, with couplings of gravitational strength “Yukawa-cut at 1/M_X” (#11 §7.5; Yukawa forces).
  • Superseded: safety through a dominant massless combination — the same replacement, recorded on constrained bimetric gravity: “safety is by range, not decoupling” (#8 §3).
  • Superseded: the graviton-mass bound as a mixing-angle check — calc note #7 §4 read the gravitational-wave bounds on a graviton mass as a check on the mixing angle → calc note #8 §3: the bounds “apply to the even eigenstate, which is exactly massless”, so they hold identically (#11 §7.5; row 6).
  • Superseded: earlier forms of the answer — Born’s answer stated more strongly: its vacuum energy “zero by theorem” (#1 addendum v0.6), Debt 1 called closed without qualification (#1 addendum v0.6; #9 §5), and “theory” the defensible word after a pass (calc note #6 §5) → #11: “its wedge vacuum energy zero by identity”, the open items of §14, and “theory” waiting on OP1–OP3.
  • Superseded: the v1 count of two standalone results — #9 §11’s “at least two results that stand on their own regardless of its fate” → #11 §15 keeps the symplectic-partner observation and counts the vacuum-energy identity as “one identity awaiting a novelty verdict”.
  • Superseded: an ad hoc branch given a reason to exist — calc note #8 §1, #1 addendum v0.6 and #9 §5: reciprocity gave the interchange-symmetric branch of bimetric gravity its “reason to exist” → #11 §7.4: the branch “appears in the partially-massless (PM) bimetric literature”, and whether reciprocity is the origin of the PM symmetry is OP2.
  • Superseded: the standalone-result claim — calc note #8 §2 expected the vacuum-energy identity, if unnoticed in the literature, to be “a standalone publishable observation”, and #9 §5 “a standalone result” → #11 §7.4 downgraded the novelty claim from “likely standalone result” to “requires detailed comparison with the PM and exchange-symmetric literature”.
  • Superseded: the cancellation framed as a cosmological-constant result — “A cosmological-constant cancellation for free, from symmetry” (#9 §5) and “by symmetry rather than tuning” (#1 addendum v0.6, queried by flag 6) → #11: the cancellation concerns the wedge sector at the aligned point and does not by itself address matter-loop vacuum energy (§7.3), and its novelty awaits comparison (§7.4).
  • Superseded: a pass as the threshold for “theory” — 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” (OP1–OP3). The tuning test’s pass stands.

Dark matter#

  • Superseded: the Gaussian gate of v0.1 — the gate e^{−k²/μ²}, its existence a postulate [P] and its Gaussian form underived (#1 §3) → the mechanism is X exchange (addendum v0.3), μ is the χ quantum’s momentum-fiber width (addendum v0.4), and the gate is an unspecified F(k²/μ²), tagged [D — mechanism; shape [O]] (#9 §6; #11 §8). The two conventions for the gate’s exponent are flag 17.
  • Superseded: earlier forms of the mechanism — μ as a scale of the momentum-space metric (#1 §3), then tied to the masses M_X and M_B “parametrically” (calc note #5 §E), and an auxiliary X delivering the gate directly (#5 §D) → μ as the χ quantum’s own width (calc note #6 §4), and a contact operator obtained by integrating out a massive, propagating X.
  • Superseded: the exponential cliff of v0.1 — σ_T(v) = σ₀e^{−v²/v*²}, “An exponential cliff, not a power-law tail” (#1 §5.1) → a knee at v* whose tail shape is open (#1 addendum v0.4; #11 §8, §13 row 1).
  • Superseded: the v0.1 predictions from the benchmark — cross-sections above the gate computed from the cliff, a cluster self-interaction “identically zero at any future sensitivity”, and two parameters covering five phenomena (#1 §5.1, §10) → #11 row 1 keeps “zero cluster signal (particle χ)” with no number; the numbers hold only for a Gaussian tail, and two of the five phenomena died.
  • Superseded: the cubic suppression of Debt 3a — “(v*/σ)³ suppression rather than an exponential” (calc note #2) → (v*/σ)⁴ (calc notes #3 and #4; #11 §9).
  • Superseded: racing stream growth against orbital stirring — the notebook’s stream growth rate against orbital phase-mixing, “the theory’s most important undone calculation on the astrophysics side” (#1 §5.2) → calc note #2: below the instability threshold there is no growth to race, “the flocking never starts”, and the benchmark misses the threshold by 28–31 orders of magnitude.
  • Superseded: Debt 3b’s ultra-faint-dwarf row — calc note #3 entered ultra-faint dwarfs with a density of 20 GeV/cm³ and a velocity dispersion of 3 km/s → calc note #4 used Segue 1’s values, ρ ≈ 100 GeV/cm³ and σ ≈ 3.7 km/s, calling the earlier density “the conservative 20 used in 3b”.
  • Superseded: reciprocity acting as modular S — #14 v2’s “load-bearing conjecture” that reciprocity acts on the hidden coupling as the modular S transformation, fixing α_d ≈ 34 → Paul’s decision of 2026-10-19 that “S-duality is no longer what fixes α_d” (review/v3-worklog.md); the candidate that needed the coupling is dead (Obituary: the coupling α_d ≈ 34).
  • Superseded: F2, which coupling sets the soliton mass — the worklog’s resolution of v2’s two couplings, a weak elementary coupling α_e,d ≈ α with heavy, strongly coupled solitons, adopted on 2026-10-19 as hypothesis H → not refuted, but superseded because hypothesis H died with the candidate.
  • Superseded: the convention and running spread — the worklog’s adjudication that the value 34 depends on a convention by a factor of 4 and is lower when the couplings are matched at a higher energy (item R2) → with hypothesis H dead, nothing in the program fixes α_d, and the spread bears on no current claim.
  • Superseded: the “point, not a window” of the v3 worklog — worklog finding F1: the Kibble estimate with p = 1 closes “at a single point, M* ≈ 3.0×10¹³ GeV”, and v3 moved its benchmark there: “This is a point, not a window.” → the (M/M*)⁴ scaling of the dilution survives, but the numbers rest on a wrong normalization (Obituary: the Kibble normalization); the record cites only the gated values.
  • Superseded: the handoff’s “current best” candidate — HANDOFF.md §2’s best dark-matter candidate, superheavy topological solitons of a separate, strongly coupled dual gauge sector, with its open items and queue items 1–3 → dead as a program-native proposal (root CLAUDE.md; #11 §12; round-3 Decision 2); queue items 1 and 2 were done and item 3 was dropped.
  • The X-condensate as a direction (in the body of the X-condensate candidate) — “[O — direction, deliberately unopened]” (#9 §10 item 7) → one of the two remaining candidates (#11 §12).

Cosmology#

  • Superseded: the earlier heuristic rule — w_eff = −2 − w̃, a heuristic of the development discussion that identified densities across frames “without the constraint’s volume Jacobian” → w_eff = −w̃ (#1 §0, §6; #11 §10). The claim built on the old rule is dead.
  • Superseded: the potential’s origin in the rigid ω — the same attribution of the potential of the dark-energy field τ to the rigid ω (#1 §3), summed up in #1 §12 as a single spontaneously broken symmetry “with a rigid symplectic form as its explicit tilt” → the potential’s periodicity [D] stands, and its origin is open (calc note #5 §F; #11 §4; root CLAUDE.md).
  • Superseded: the earlier readings of DESI — #1, #9, HANDOFF.md §2, #14 v3, both popular articles and the italic passage of #11 §10 read the instrument’s results as support for the drift → “under real pressure” (root CLAUDE.md; #11 §10, “Under pressure (v2.1)”; round-3 ruling 11), since its second data release favours a phantom crossing above z ≈ 0.4. The italic passage of #11 §10 was not updated.

Predictions#

  • Superseded: the exponential cliff of v0.1 — row 1 as a cliff, “exactly zero in clusters forever” (#1 §9) → “Knee at v* ~ 10² km/s; zero cluster signal (particle χ)” (#11 §13).
  • Superseded: the exponential and the cube — row 3’s “exponential” particle side, and calc note #2’s (v*/σ)³ for the wave side → “sharp” against (v*/σ)⁴ (#9 §7; #11 §9, §13).
  • Superseded: DESI read as support — row 4’s side of the same change: the documents read the survey’s hints as confirmation of the drift → the technical record of #11 §10 and the root CLAUDE.md.
  • Superseded: “after V(τ) < 0” — row 5’s “Turnaround after V(τ) < 0 = conjugate bounce” (#9 §9) → “Turnaround = conjugate bounce” (#11 §13); no document says why the clause was dropped, and the sign of V is flag 27.
  • Superseded: “not previously posed” — #9 §11 counted the masslessness of the even eigenstate among its “novel predictions not previously posed” → #11 §15 names only rows 3 and 11; no document says why.
  • Superseded: earlier forms of the row — row 7’s permanent null, first for χ (#1 §9), then for χ or the X-condensate (#9 §9), then for all three candidates of #11 v2.0 → for “both dark-sector candidates”, with P4 strict (#11 v2.1, v2.2).
  • Superseded: the spectral step and the ±0.03 target — #1’s row 10, with a step in the gravitational-wave spectrum and a target of ±0.03 in N_eff for the cosmic microwave background experiment CMB-S4 → v1 dropped both (#9 §9), and #11 kept v1’s form; no document says why.
  • Superseded: the three-way question — particles, X-condensate or solitons (#11 v2.0; HANDOFF.md §2 item 8) → two candidates since #11 v2.1, after round-3 Decision 2 (dark-sector candidates).
  • Superseded: the parameter count — #1 §10’s two parameters per sector → #11 keeps only the dark-energy row, as the over-constraint, and has no full parameter table; in the X sector five βₙ reduce to two (calc note #8 §3; #11 §7.5).
  • The predictions tables (in the body of history of the predictions table) — the ten rows of #1 §9, with rows 1, 3 and 7 “the flagship discriminants”, and the ten of #9 §9 → the eleven of #11 §13; old rows 3 and 4 are dead, as obituaries in the graveyard.

Method and review#

  • [T] as “theorem — established in the literature, cited” (#1 §0) → [T] as “established literature”, with [V], [S] and † added (#11 header); in the body of provenance tags and citation marks.
  • The pre-registration record “scored 2-for-2 on verdicts” (HANDOFF.md §5) → rounds 1–2 hit, round 3 missed and round 4 hit (review/round4-adjudication.md, “Pre-registration scored”); in the body of pre-registration and its calibration record.
  • “Round 3 (incomplete)” (HANDOFF.md §6), with its partial finding “citations and core numbers check out so far” → completed with verdict C (review/round3-adjudication.md; root CLAUDE.md); in the body of Review round 3.
  • The gate’s check of #14, knot_numbers.py, written to recompute the numbers of v2 and then v3 → verify/soliton_obituary.py, which “checks every number this record quotes, with independent anchors” (review/round3-adjudication.md) (flag 33 in review/wiki-build-flags.md: its checks cover less than this; see what it does not check); in the body of the soliton-obituary script.

History and documents#

  • HANDOFF.md §3’s statuses, #11 as v2.0, the current reference, and #14 as v2, the current blind-review manuscript → #11 v2.2, and #14 v3, withdrawn after failing the round-3 review (root CLAUDE.md, “Layout”); in the body of the handoff document.
  • HANDOFF.md §3’s read order, #11 → #14 → HANDOFF.md §6 → calc notes → the root CLAUDE.md’s #11 → HANDOFF.md §6 → review/round3-adjudication.md → calc notes “only as a task needs them”; in the body of CLAUDE.md and the README.
  • HANDOFF.md §8’s ranked queue → the root CLAUDE.md’s queue, on open problems and the queue.
  • HANDOFF.md §9’s suggested repository layout → the layout recorded in the root CLAUDE.md, “Layout”.
  • The root CLAUDE.md’s “#11 is now v2.1” → v2.2, as a later bullet of the same section says (flag 38).
  • The README.md tagline, “Physics hypothesis explaining dark matter and missing magnetic monopoles” → not rewritten, but overtaken by the record: the monopole explanation is dead (#11 §11.1), the dark-matter candidates are open (#11 §12), and the root CLAUDE.md calls the program “a Lakatosian research program, not a theory” (flag 37).

Sources#

  • CLAUDE.md “Since the handoff”, “Layout” — the soliton candidate dead; the current queue, read order and layout; “#11 is now v2.1”.
  • papers/broken-born-checkpoint-v2.md header, §4, §5, §7, §8, §10, §12, §13, §14, §15 — the current forms and their version notes.
  • papers/reciprocity-toy-models.md §1, §4, §5 — the toy-model note’s v2 wording.
  • review/round4-adjudication.md “Rulings”, “Pre-registration scored”, “Revisions for v2 of the note” — the corrections to the note’s first version; the calibration record.
  • review/round3-adjudication.md “Decisions” — the retired candidate; the replacement gate script.
  • HANDOFF.md §2, §3, §5, §6, §8, §9 — the handoff’s statements that later sources replaced.
  • notes/broken-born-theory.md §0–§12 and addenda v0.2–v0.6 — the version-0.1 forms and their corrections.
  • notes/broken-born-program-v1.md §2–§11 — v1.0’s forms.
  • notes/debt1a-geometric-core.md §B–§F, notes/debt1a-ii-X-classification.md §1–§5, notes/debt1a-iii-tuning-test.md §4, notes/debt1a-iv-beta-coefficients.md §1–§3 — the classification of X, the gate scale, the safety argument and the novelty claims.
  • notes/debt3a-stream-stability.md, notes/debt3b-wave-island.md, notes/debt3c-ufd-endpoint.md — the cubic suppression, the race against stirring, the ultra-faint-dwarf row.
  • notes/toy-lagrangian.md “Chunk 2 results”, “Assessment against the predictions” — the reversed sign; the first verdict.
  • review/v3-worklog.md “Findings neither referee raised”, “Round-2 pending list” — F1, F2 and R2; the decision that S-duality no longer fixes α_d.
  • review/wiki-build-flags.md items 6, 10, 11, 17, 27, 33, 37, 38 — the flagged statements named above.
  • README.md — the tagline.
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