Gravity Seven Gaps Full Theory Ledger Pillar1 And Pillar2 Closed Pillar3 Open

The three pillars

A full physical theory, in the strongest sense, must clear three hurdles. First, it must recover the known classical world: from a discrete substrate, it must produce Einstein's equations in the smooth four-dimensional limit, in action, operator, and constraint forms. Second, it must supply a well-defined quantum amplitude: a derived bridge from substrate to geometry, a measure that comes from the substrate, and a path-sum limit under mesh refinement. Third, it must make at least one confirmed prediction that distinguishes it from the standard model of cosmology by a stated number of measurement sigmas, with the inference running from theory to data. The first two hurdles concern derivation; the third concerns experiment.

Recognition Science tracks these hurdles in a machine-checked library of formal theorems, a collection where every proof is verified by a computer kernel. The library keeps a ledger, a discrete record of boolean flags, one per benchmark. A flag flips to true only when its target theorem is kernel-checked, axiom-audited, and critic-passed, or when the project leader adopts a target as a foundational model. The master theorem full_theory_open_pillar3_alone states that the full theory is not closed, that pillars 1 and 2 are closed, and that pillar 3 is not. The declaration pillar1_and_pillar2_closed_pillar3_open is a direct consequence, isolating the remaining open obligation.

The closure criterion itself is a definition, not a theorem, so the claim cannot drift from the flags. The criterion was audited in 2026-07-26, and six defects were found and repaired. The defects were all of one kind: the old criterion checked that a statement had been proved, but never that the proved statement was the promised one. For example, pillar 1 never asked where the Regge discretization came from, and pillar 2 would have flipped on a complexity cutoff that is not a continuum limit. The repaired criterion is strictly stronger, and the repair is itself kernel-checked against four decoys plus a positive control. The consequence is that pillar 1 is open again under the repaired criterion, though the three recovery strengths still hold.

What the declaration does not claim is as precise as what it claims. It does not claim that the full theory is closed, nor that any pillar is closed at derivation strength beyond the flags that have flipped. It does not claim that pillar 3's prediction exists, only that it remains open. It does not claim that the flags themselves are theorems; they are records, and the criterion is a definition. The ledger's value is that the state of the campaign is transparent: two pillars stand, one remains, and the remaining one is a discriminating prediction that no one has yet produced.

/-- **PILLARS 1 AND 2 CLOSED, Pillar 3 open, 2026-07-31 (the D-A day).**
Pillar 1 closed when `gap1_provenance_derived` flipped under Jon's D-A
ruling: its provenance conjunct holds at MODEL strength under the named
adoptions (never derived), on top of the four recovery strengths at theorem
strength (`classical_recovery_strengths_hold`). Pillar 2 closed the same
day (flag 9, at derived action shape plus MODEL super-critical strength).
Pillar 3 stays open: both flag-11 conjuncts are `false`, with residual
E_lat and the sky. Nothing was un-proved to produce either closure, and no
Boolean was flipped down. Renamed from
`pillar1_and_pillar3_open_pillar2_closed` the day Pillar 1 closed. -/
theorem pillar1_and_pillar2_closed_pillar3_open :
    Pillar1Closed fullTheoryBenchmarks ∧
    Pillar2Closed fullTheoryBenchmarks ∧
    ¬ Pillar3Closed fullTheoryBenchmarks :=
  full_theory_open_pillar3_alone.2

/-- **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

/-- **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 live record is rejected by the repaired criterion for the two
flag-11 conjuncts alone.** A reader can see from the flags alone where
every remaining obligation sits, which is the property the pre-repair
criterion did not have. `gap2_measure_derived` left this list on
2026-07-30 (flag 8, gatekeeper-signed), `gap2_geometric_continuum_limit`
on 2026-07-31 (flag 9, Jon's criterion ruling, `Gap2GaugeTransport`), and
`gap1_provenance_derived` and `no_free_constants` on 2026-07-31 (flags 6
and 12, closed at MODEL strength under Jon's D-A adoptions, never derived).
What remains is Pillar 3: the discriminating prediction, whose residual is
E_lat and the sky. -/
theorem live_record_open_obligations :
    fullTheoryBenchmarks.discriminating_prediction_confirmed = false ∧
    fullTheoryBenchmarks.prediction_is_discriminating = false :=
  ⟨rfl, rfl⟩

What this page does not claim

The full theory is closed. Pillar 3's prediction exists. The flags themselves are theorems; they are records. The framework has derived the fine-structure constant.

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)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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