Gravity Seven Gaps Full Theory Ledger Repaired Criterion Is Strictly Stronger

The repaired criterion

In 2026, the Recognition Science research program's campaign to build a full quantum gravity theory faced a bookkeeping problem. The campaign kept a machine-checked ledger of progress, with one boolean flag per major benchmark. The master theorem that the full theory remains open stayed provable until every flag flipped to true. The load-bearing object was not the flags themselves but the closure criterion, the definition of what counts as 'full theory complete'. An audit found six defects in that criterion, all of the same kind: it checked that a statement had been proved, but never that the proved statement was the promised one.

The repaired criterion, named FullTheoryClosed, is a definition that now demands more than the legacy version. For the first pillar, classical recovery, it now requires that the origin of the discrete discretization be derived, not stipulated. For the second pillar, the quantum amplitude, it demands a derived measure and a genuine geometric continuum limit, not merely a complexity cutoff. For the third pillar, a discriminating prediction, it requires both that a prediction is confirmed and that it actually discriminates from the incumbent theory. It also adds a fourth condition: no free real constant in any closer.

The theorem repaired_criterion_is_strictly_stronger proves that this new criterion is genuinely stricter. It exhibits four benchmark configurations that satisfy the legacy closure criterion but fail the repaired one: a 'laundry' list that passes the old checks without substance, a 'cutoff only' configuration that would have flipped pillar 2 on a complexity cutoff, a 'weak prediction' that agrees with the incumbent without discriminating, and a 'free constant' configuration that leaves a parameter unpinned. For each, the theorem proves the legacy criterion holds while the repaired one does not. It also proves the positive control: the ideal benchmark configuration satisfies both. The proof is machine-checked, with zero unproven axioms.

What this does not claim is that the full theory is closed. The live record shows pillar 1 and pillar 2 are closed, but pillar 3, the discriminating prediction, remains open. The theorem only proves the criterion is stricter, not that the stricter criterion is met. It also does not claim that the four flawed configurations are the only possible failures, or that the repaired criterion is the final word. It is a repair of a specific defect, not a proof of the theory itself.

/-- **The gate discriminates: strictness.** All four decoys close under the
pre-repair criterion and fail under the repaired one, each for its own defect,
while the positive control closes under both. A gate that rejected everything
would satisfy `repaired_criterion_implies_legacy` vacuously; the last conjunct
is what rules that out. -/
theorem repaired_criterion_is_strictly_stronger :
    (LegacyFullTheoryClosed laundryBenchmarks ∧
      ¬ FullTheoryClosed laundryBenchmarks) ∧
    (LegacyFullTheoryClosed cutoffOnlyBenchmarks ∧
      ¬ FullTheoryClosed cutoffOnlyBenchmarks) ∧
    (LegacyFullTheoryClosed weakPredictionBenchmarks ∧
      ¬ FullTheoryClosed weakPredictionBenchmarks) ∧
    (LegacyFullTheoryClosed freeConstantBenchmarks ∧
      ¬ FullTheoryClosed freeConstantBenchmarks) ∧
    (LegacyFullTheoryClosed idealBenchmarks ∧
      FullTheoryClosed idealBenchmarks) :=
  ⟨⟨laundry_closes_legacy, laundry_fails_repaired⟩,
    ⟨cutoffOnly_closes_legacy, cutoffOnly_fails_repaired⟩,
    ⟨weakPrediction_closes_legacy, weakPrediction_fails_repaired⟩,
    ⟨freeConstant_closes_legacy, freeConstant_fails_repaired⟩,
    ⟨ideal_closes_legacy, idealBenchmarks_closes⟩⟩

/-- **THE CLOSURE CRITERION (live, repaired 2026-07-26).** The full theory in
the strongest sense is closed when all three pillars close *and* no free real
constant remains in any pillar closer (D4). Parameter-freeness is a
conjunct rather than a footnote because it is the claim the whole program is
named for, and an unpinned constant silently absorbs any disagreement the
pillars would otherwise have to face. -/
def FullTheoryClosed (b : FullTheoryBenchmarks) : Prop :=
  Pillar1Closed b ∧ Pillar2Closed b ∧ Pillar3Closed b ∧
    b.no_free_constants = true

/-- **MASTER THEOREM (the honest gate), replaced 2026-07-31 after the D-A
adoptions.** The full theory is NOT closed, and the obstruction is Pillar 3
alone: `discriminating_prediction_confirmed = false` and
`prediction_is_discriminating = false` (flag 11; its residual is E_lat and
the sky). The strength of every closed conjunct: flag 6
(`gap1_provenance_derived`) and flag 12 (`no_free_constants`) closed
2026-07-31 at MODEL strength under the named D-A adoptions (MODEL 1-L and
the SameLatticeUnitsPremise, on top of the already adopted MODEL 1 and
MODEL 2; never derived, the derivation routes kernel-proved dead), composed
in `Gap5UnitIdentificationsAdopted`; Pillar 2 closed 2026-07-31 with flag 9
at derived action shape plus MODEL super-critical strength
(D-qg-flag9-closes-at-model-strength-20260731) on top of the bridge and
measure flags at theorem strength; the four recovery flags of Pillar 1
stand at theorem strength. This theorem replaces `full_theory_not_yet_closed`,
retired the day pillars 1 and 2 closed because its recorded premise (two
pillars open) stopped being true; it fails to build unchanged the moment
flag 11 flips, so it cannot silently coexist with a closure claim. -/
theorem full_theory_open_pillar3_alone :
    ¬ FullTheoryClosed fullTheoryBenchmarks ∧
      Pillar1Closed fullTheoryBenchmarks ∧
        Pillar2Closed fullTheoryBenchmarks ∧
          ¬ Pillar3Closed fullTheoryBenchmarks := by
  refine ⟨?_, ⟨rfl, rfl, rfl, rfl, rfl⟩, ⟨rfl, rfl, rfl, rfl⟩, fun h => ?_⟩
  · intro h
    have := h.2.2.1.1
    simp [fullTheoryBenchmarks] at this
  · have := h.1
    simp [fullTheoryBenchmarks] at this

What this page does not claim

The full theory is closed. The four flawed configurations are the only possible failures of the legacy criterion. The repaired criterion is the final or complete definition of a full theory.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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