Encyclopedia Gravity Gravity Seven Gaps Campaign Ledger Seven Gaps Campaign Status

ARTICLE 4 claims 4 theorems

Gravity Seven Gaps Campaign Ledger Seven Gaps Campaign Status

A machine-checked status record that separates what a 2026 research campaign proved from what it left open, gap by gap.

Verify this page

Campaign status ledger

The SevenGapsCampaignStatus is a machine-checked status record, a ledger (a discrete record of events and their outcomes) for a 2026-07-14/15 research campaign in Recognition Science. The campaign attacked seven named gaps in a program to derive gravity from a discrete recognition substrate. The declaration's purpose is to state, for each gap, what was proved and what remains open. It does not flip any full-strength closure flags; it is a scoped-increment record, not a claim of complete physical closure.

For each of the seven gaps, the ledger records a proved increment and an open residual. Gap 1, the substrate-to-triangulation map, proved two obstruction theorems against an assumed raw-deficit form, and closed its Hessian-symbol comparison on 2026-07-22 under amended intent. Gap 2 proved count-finiteness of a bounded combinatorial class for the path-sum measure, but the continuum limit remains open. Gap 3 proved a rank bound on the conformal image of the tensor sector, but the full TT polarization decomposition on the torus remains open. Gap 4 proved flat TT eigenvalue convergence for the axis stencil sector only, not isotropic flat-space recovery; the direction-resolved symbol and curved backgrounds remain open. Gap 5 proved a discrete hypersurface-deformation relation closing on a Wronskian-smeared momentum density, with the continuum Dirac algebra and HKT rigidity closed on 2026-07-23. Gap 6 defined 3D CDT causal classes and proved exact Euclideanized non-degeneracy thresholds, with the 4D action-level Wick continuation closed on 2026-07-23. Gap 7 proved a machine-checked constraint on a bridge-and-ansatz conjunction, but the true second-order mechanism remains open.

The theorem no_full_physical_closure_claimed is the ledger's spine. It states, by reflexivity against the imported modules, that gaps 2, 3, and 7 retain an explicit OPEN component, while gaps 1, 4, 5, and 6 have their open flags set to false. The theorem campaign_flags_anchored re-derives one load-bearing campaign-era result per gap directly from the imported modules, so the ledger cannot silently drift from the artifacts. These anchors date from the 2026-07-14/15 lattice campaign; the gap-5 conjunct is the abelian momentum-sector instance from that campaign, NOT the 2026-07-23 close.

What the ledger does not claim is as important as what it proves. It does not claim full physical closure for any gap; each increment is scoped, and the open residuals are explicit. It does not claim that the axis-sector convergence in gap 4 is isotropic flat-space recovery; the anisotropic moment tensor A0 = (1+sqrt 2) I + (sqrt 2 + sqrt 3) J is invisible to axis stencils. It does not claim that the campaign-era gap-5 anchor is the terminal 2026-07-23 close; that binding lives in a separate module to avoid an import cycle. The status record is a honest tier list: proved increments and open residuals, side by side, with no conflation.

THEOREM SevenGapsCampaignStatus · IndisputableMonolith/Gravity/SevenGaps/CampaignLedger.lean
SevenGapsCampaignStatus · IndisputableMonolith/Gravity/SevenGaps/CampaignLedger.lean:106 
/-- Per-gap campaign status: what the 2026-07-14/15 campaign proved and what
remains open toward full physical closure. -/
structure SevenGapsCampaignStatus where
  gap1_sign_and_parity_nogos_proved : Bool
  gap1_quadratic_energy_bridge_constructed : Bool
  gap1_hessian_symbol_comparison_open : Bool
  gap2_count_finiteness_proved : Bool
  gap2_measure_and_invariance_proved : Bool
  gap2_continuum_limit_open : Bool
  gap3_conformal_subspace_proper_proved : Bool
  gap3_shear_witness_constructed : Bool
  gap3_full_tt_decomposition_open : Bool
  /-- Flat TT eigenvalue convergence proved for the AXIS stencil sector
  only; not isotropic flat-space recovery (Test G anisotropic moment tensor
  `A0 = (1+sqrt 2) I + (sqrt 2 + sqrt 3) J`; see module header, gap 4). -/
  gap4_flat_tt_convergence_proved : Bool
  gap4_curved_qnm_open : Bool
  gap5_lattice_dirac_relations_proved : Bool
  gap5_continuum_algebra_hkt_open : Bool
  gap6_kinematical_wick_certified : Bool
  gap6_action_continuation_open : Bool
  gap7_seam_grammar_verdict_certified_miss : Bool
  gap7_true_mechanism_open : Bool
THEOREM no_full_physical_closure_claimed · IndisputableMonolith/Gravity/SevenGaps/CampaignLedger.lean
no_full_physical_closure_claimed · IndisputableMonolith/Gravity/SevenGaps/CampaignLedger.lean:150 
/-- The campaign did not achieve (and does not claim) full physical closure:
gaps 2/3/7 retain an explicit OPEN component. Gap 1's hessian-symbol
comparison closed 2026-07-22 under amended intent
(`gap1_hessian_join_closing_package`); gap6 action continuation closed
2026-07-23 via `wick_action_continuation_4d_v2`; gap4 curved/QNM closed
2026-07-23 via `discrete_tt_spectrum_converges_curved` ∧
`quasinormal_mode_spectrum`; gap5 continuum algebra + HKT closed 2026-07-23
via `dirac_algebra_continuum_limit` ∧ `hojman_pins_general_relativity`.
This theorem tracks the remaining opens plus the closed bits. -/
theorem no_full_physical_closure_claimed :
    sevenGapsCampaignStatus.gap1_hessian_symbol_comparison_open = false
      ∧ sevenGapsCampaignStatus.gap2_continuum_limit_open = true
      ∧ sevenGapsCampaignStatus.gap3_full_tt_decomposition_open = true
      ∧ sevenGapsCampaignStatus.gap4_curved_qnm_open = false
      ∧ sevenGapsCampaignStatus.gap5_continuum_algebra_hkt_open = false
      ∧ sevenGapsCampaignStatus.gap6_action_continuation_open = false
      ∧ sevenGapsCampaignStatus.gap6_kinematical_wick_certified = true
      ∧ sevenGapsCampaignStatus.gap7_true_mechanism_open = true :=
  ⟨rfl, rfl, rfl, rfl, rfl, rfl, rfl, rfl⟩
THEOREM campaign_flags_anchored · IndisputableMonolith/Gravity/SevenGaps/CampaignLedger.lean
campaign_flags_anchored · IndisputableMonolith/Gravity/SevenGaps/CampaignLedger.lean:170 
/-- **Anchor theorem (campaign-era).**  The proved flags are not
free-floating booleans: this theorem re-derives one load-bearing
campaign-era result per gap directly from the imported modules, so the
ledger cannot silently drift from the artifacts.  These anchors date from
the 2026-07-14/15 lattice campaign; in particular the gap-5 conjunct is the
abelian momentum-sector instance from that campaign, NOT the 2026-07-23
close.  The closed gap-5 terminal binding lives in
`Gap5ConstraintCloseStatus.gap5_constraint_recovery_bound_to_terminals`
(kept out of this module to avoid an import cycle).
(Gap 7 is quarantined and anchored in `SeamGrammarVerdict` itself.) -/
theorem campaign_flags_anchored :
    -- gap 1 (sign no-go: every bridge forces nonnegative deficits)
    (∀ {Λ : Type} [inst : Fintype Λ] [inst2 : DecidableEq Λ]
      (L : RecognitionLedger.RecognitionLedger Λ) (H : Type)
      (b : LedgerToHingeBridge H L) (i : Λ),
        0 ≤ b.geometricDeficit (b.x_sigma i))
    -- gap 2 (count-finiteness of the scoped class)
    ∧ (∀ B : ℕ, 0 < Fintype.card (PathSumMeasure.BoundedComplex B))
    -- gap 4 (flat TT eigenvalue convergence for every fixed AXIS mode;
    -- axis sector only, see the gap-4 scope note in the module header)
    ∧ (∀ k : ℕ, Filter.Tendsto
        (fun N : ℕ => 4 * (N : ℝ) ^ 2 * Real.sin (Real.pi * k / N) ^ 2)
        Filter.atTop (nhds ((2 * Real.pi * k) ^ 2)))
    -- gap 5 (abelian momentum sector, n = 8 instance; campaign-era anchor,
    -- the 2026-07-23 terminal close is bound in Gap5ConstraintCloseStatus)
    ∧ (∀ (a b : ZMod 8) (x : HypersurfaceDeformation.PhaseSpace 8),
        HypersurfaceDeformation.bracket (HypersurfaceDeformation.Dgen a)
          (HypersurfaceDeformation.Dgen b) x = 0)
    -- gap 6 (exact non-degeneracy iff on the causal class)
    ∧ (∀ (ty : CausalSimplexWick.CausalTetType) (a alpha : ℝ), 0 < a →
        (0 < Geometry.CayleyMengerPolynomial.cm3
            (CausalSimplexWick.euclideanSqEdges ty a alpha)
          ↔ CausalSimplexWick.alphaMin ty < alpha)) := by
  refine ⟨?_, ?_, ?_, ?_, ?_⟩
  · intro Λ _ _ L H b i
    exact bridge_forces_nonneg_geometricDeficit L b i
  · exact PathSumMeasure.boundedComplex_card_pos
  · intro k
    simpa [DiscreteLichnerowicz.discreteEigenvalue] using
      DiscreteLichnerowicz.discreteEigenvalue_tendsto k
  · intro a b x
    exact HypersurfaceDeformation.bracket_Dgen_Dgen a b x
  · intro ty a alpha ha
    exact CausalSimplexWick.cm3_euclidean_pos_iff ty a alpha ha
THEOREM campaign_flags_anchored · IndisputableMonolith/Gravity/SevenGaps/CampaignLedger.lean
campaign_flags_anchored · IndisputableMonolith/Gravity/SevenGaps/CampaignLedger.lean:170 
/-- **Anchor theorem (campaign-era).**  The proved flags are not
free-floating booleans: this theorem re-derives one load-bearing
campaign-era result per gap directly from the imported modules, so the
ledger cannot silently drift from the artifacts.  These anchors date from
the 2026-07-14/15 lattice campaign; in particular the gap-5 conjunct is the
abelian momentum-sector instance from that campaign, NOT the 2026-07-23
close.  The closed gap-5 terminal binding lives in
`Gap5ConstraintCloseStatus.gap5_constraint_recovery_bound_to_terminals`
(kept out of this module to avoid an import cycle).
(Gap 7 is quarantined and anchored in `SeamGrammarVerdict` itself.) -/
theorem campaign_flags_anchored :
    -- gap 1 (sign no-go: every bridge forces nonnegative deficits)
    (∀ {Λ : Type} [inst : Fintype Λ] [inst2 : DecidableEq Λ]
      (L : RecognitionLedger.RecognitionLedger Λ) (H : Type)
      (b : LedgerToHingeBridge H L) (i : Λ),
        0 ≤ b.geometricDeficit (b.x_sigma i))
    -- gap 2 (count-finiteness of the scoped class)
    ∧ (∀ B : ℕ, 0 < Fintype.card (PathSumMeasure.BoundedComplex B))
    -- gap 4 (flat TT eigenvalue convergence for every fixed AXIS mode;
    -- axis sector only, see the gap-4 scope note in the module header)
    ∧ (∀ k : ℕ, Filter.Tendsto
        (fun N : ℕ => 4 * (N : ℝ) ^ 2 * Real.sin (Real.pi * k / N) ^ 2)
        Filter.atTop (nhds ((2 * Real.pi * k) ^ 2)))
    -- gap 5 (abelian momentum sector, n = 8 instance; campaign-era anchor,
    -- the 2026-07-23 terminal close is bound in Gap5ConstraintCloseStatus)
    ∧ (∀ (a b : ZMod 8) (x : HypersurfaceDeformation.PhaseSpace 8),
        HypersurfaceDeformation.bracket (HypersurfaceDeformation.Dgen a)
          (HypersurfaceDeformation.Dgen b) x = 0)
    -- gap 6 (exact non-degeneracy iff on the causal class)
    ∧ (∀ (ty : CausalSimplexWick.CausalTetType) (a alpha : ℝ), 0 < a →
        (0 < Geometry.CayleyMengerPolynomial.cm3
            (CausalSimplexWick.euclideanSqEdges ty a alpha)
          ↔ CausalSimplexWick.alphaMin ty < alpha)) := by
  refine ⟨?_, ?_, ?_, ?_, ?_⟩
  · intro Λ _ _ L H b i
    exact bridge_forces_nonneg_geometricDeficit L b i
  · exact PathSumMeasure.boundedComplex_card_pos
  · intro k
    simpa [DiscreteLichnerowicz.discreteEigenvalue] using
      DiscreteLichnerowicz.discreteEigenvalue_tendsto k
  · intro a b x
    exact HypersurfaceDeformation.bracket_Dgen_Dgen a b x
  · intro ty a alpha ha
    exact CausalSimplexWick.cm3_euclidean_pos_iff ty a alpha ha

What this page does not claim

Full physical closure for any of the seven gaps. Isotropic flat-space recovery from the axis-sector convergence in gap 4. That the campaign-era gap-5 anchor is the terminal 2026-07-23 close.

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/CampaignLedger.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.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red:

MACHINE LAYER · GROUNDED CLAIM TABLE · CLICK TO EXPAND