IndisputableMonolith.Gravity.SevenGaps.CampaignLedger

   1import IndisputableMonolith.Gravity.SevenGaps.LedgerBridgeNoGo
   2import IndisputableMonolith.Gravity.SevenGaps.LedgerEnergyBridge
   3import IndisputableMonolith.Gravity.SevenGaps.PathSumMeasure
   4import IndisputableMonolith.Gravity.SevenGaps.EdgeTensorSector
   5import IndisputableMonolith.Gravity.SevenGaps.DiscreteLichnerowicz
   6import IndisputableMonolith.Gravity.SevenGaps.HypersurfaceDeformation
   7import IndisputableMonolith.Gravity.SevenGaps.CausalSimplexWick
   8
   9/-!
  10# Seven-Gaps Campaign Ledger (2026-07-14/15)
  11
  12Machine-checked status record of the QG seven-gaps campaign, in the style of
  13`Gravity.QGScopeAudit`.  One flag pair per gap: what the campaign PROVED
  14(scoped increment, kernel-checked in the imported modules), and what remains
  15OPEN toward full physical closure.  This module intentionally does NOT flip
  16any `QGScopeAudit` closure flag: those record the full-strength closures, and
  17none of the increments below is a full-strength closure.
  18
  19## Per-gap summary (weakest-link honest tiers)
  20
  211. **Substrate-to-triangulation map.**  `LedgerBridgeNoGo` proves two
  22   obstruction theorems against the assumed raw-deficit form: every
  23   `LedgerToHingeBridge` forces nonnegative geometric deficits on the image
  24   of the comparison map (sign no-go), and every parity-covariant J-ratio
  25   ledger family has deficit even in the deformation parameter, excluding
  26   signed linear response (parity no-go).  Under the geometric premise
  27   (prose tier) that two-sided weak-field classes carry negative image
  28   deficits with odd leading response, the assumed form is excluded on such
  29   classes.  The corrected target is built in `LedgerEnergyBridge`:
  30   coboundary-strain J-ledger (proved `RecognitionLedger`), two-sided
  31   quadratic matching with explicit constants, strictly positive pure-shear
  32   witness; the canonical instance certifies shape-compatibility, with the
  33   independent-geometry comparison OPEN.  OPEN: Hessian-symbol comparison
  34   against the frozen Regge quadratic functional on the periodic Freudenthal
  35   mesh; tensor multichannel escalation.
  362. **Path-sum measure.**  `PathSumMeasure` proves count-finiteness of the
  37   scoped bounded combinatorial class (replacing the assumed `growthBase`),
  38   the relabeling Setoid with finite quotient, the `1/|Aut|` measure with
  39   `0 < mu <= 1` and relabeling invariance, and the unit-modulus `Z_RS`
  40   bound.  OPEN: continuum limit as the size cap grows; substrate-derived
  41   nonuniform measure.
  423. **Tensor sector.**  `EdgeTensorSector` proves the conformal image has
  43   rank at most nV on any `Triangulation3D`; on the N = 5 periodic
  44   Freudenthal torus (nV = 125 < nE = 875) the conformal subspace is proper,
  45   with an explicit face-shear witness proved non-conformal and lying in the
  46   orthogonal complement of the conformal slice.  OPEN: full TT polarization
  47   decomposition on the torus.
  484. **Operator convergence.**  `DiscreteLichnerowicz` proves the discrete
  49   Laplacian eigenvalue identity and the convergence
  50   `4 N^2 sin^2 (pi k / N) -> (2 pi k)^2` for every fixed AXIS mode, with
  51   exact discrete transversality for the two standard polarizations (MODEL:
  52   on the flat background the Lichnerowicz operator is `-Laplacian` on TT
  53   modes).  AXIS SECTOR ONLY (re-tag 2026-07-15, panel mandate C14): Test G
  54   (`Gravity.Analysis.FreudenthalStencilPreflight` /
  55   `FreudenthalEnergyLimit`, commits 7b808f75b4, 1d3ed6da06) kernel-proved
  56   the canonical Freudenthal frozen quadratic energy has the ANISOTROPIC
  57   continuum moment tensor `A0 = (1+sqrt 2) I + (sqrt 2 + sqrt 3) J`, which
  58   axis stencils cannot see; this gap-4 increment must not be read as
  59   isotropic flat-space recovery.  The direction-resolved symbol question
  60   is governed by the C10 probe (plan receipt P-iso, 2026-07-15).
  61   OPEN: direction-resolved (non-axis) symbol; curved backgrounds;
  62   quasinormal-mode spectra.
  635. **Constraint closure.**  `HypersurfaceDeformation` proves, on the
  64   finite-dimensional lattice phase space with an honest fderiv Poisson
  65   bracket: `{D_a, D_b} = 0` exactly; the forward-difference closure anomaly;
  66   exact translation invariance for the symmetric generator
  67   `{Dsym_a, H[1]} = 0`; the advection relation `{Dsym_a, H[N]}`; and the
  68   discrete hypersurface-deformation relation `{H[N], H[M]}` closing on a
  69   Wronskian-smeared momentum density.  OPEN: continuum Dirac algebra;
  70   Hojman-Kuchar-Teitelboim rigidity (typed target deliberately uninhabited).
  716. **Lorentzian sector.**  `CausalSimplexWick` defines the 3D CDT causal
  72   classes, proves the Wick involution acts as `alpha -> -alpha`, and proves
  73   exact Euclideanized non-degeneracy thresholds (`alpha > 1/3` for (3,1),
  74   `alpha > 1/2` for (2,2)) with degeneracy exactly at threshold and
  75   Lorentzian non-realizability.  OPEN: action-level continuation (complex
  76   dihedral angles, sinh/boost sector).
  777. **Discriminating prediction.**  `Constants.AlphaGenesis.SeamGrammar` +
  78   `SeamGrammarVerdict` (not imported here; the verdict module is
  79   quarantined because it references the measured constant): the seam
  80   functional `12 (sinh x - x)` derived with full numeral provenance MISSES
  81   the closing load with certified separation, and NO integer count of the
  82   odd seam excess closes (the closing load lies strictly between the 11-
  83   and 12-count members).  The verdict is a machine-checked CONSTRAINT on
  84   the bridge-and-ansatz conjunction, per the joint-prediction protocol.
  85   OPEN: the true second-order mechanism (effective non-integer seam weight
  86   forced by geometry); the O2 tail prediction is registered.
  87
  88STATUS: THEOREM for every proved flag below (forced by rfl against the
  89imported modules); the campaign-level claim is scoped increments, never full
  90physical closure.  No sorry, no new axioms in this module.
  91-/
  92
  93namespace IndisputableMonolith
  94namespace Gravity
  95namespace SevenGaps
  96namespace CampaignLedger
  97
  98/-- Per-gap campaign status: what the 2026-07-14/15 campaign proved and what
  99remains open toward full physical closure. -/
 100structure SevenGapsCampaignStatus where
 101  gap1_sign_and_parity_nogos_proved : Bool
 102  gap1_quadratic_energy_bridge_constructed : Bool
 103  gap1_hessian_symbol_comparison_open : Bool
 104  gap2_count_finiteness_proved : Bool
 105  gap2_measure_and_invariance_proved : Bool
 106  gap2_continuum_limit_open : Bool
 107  gap3_conformal_subspace_proper_proved : Bool
 108  gap3_shear_witness_constructed : Bool
 109  gap3_full_tt_decomposition_open : Bool
 110  /-- Flat TT eigenvalue convergence proved for the AXIS stencil sector
 111  only; not isotropic flat-space recovery (Test G anisotropic moment tensor
 112  `A0 = (1+sqrt 2) I + (sqrt 2 + sqrt 3) J`; see module header, gap 4). -/
 113  gap4_flat_tt_convergence_proved : Bool
 114  gap4_curved_qnm_open : Bool
 115  gap5_lattice_dirac_relations_proved : Bool
 116  gap5_continuum_algebra_hkt_open : Bool
 117  gap6_kinematical_wick_certified : Bool
 118  gap6_action_continuation_open : Bool
 119  gap7_seam_grammar_verdict_certified_miss : Bool
 120  gap7_true_mechanism_open : Bool
 121
 122/-- The campaign outcome. -/
 123def sevenGapsCampaignStatus : SevenGapsCampaignStatus where
 124  gap1_sign_and_parity_nogos_proved := true
 125  gap1_quadratic_energy_bridge_constructed := true
 126  gap1_hessian_symbol_comparison_open := true
 127  gap2_count_finiteness_proved := true
 128  gap2_measure_and_invariance_proved := true
 129  gap2_continuum_limit_open := true
 130  gap3_conformal_subspace_proper_proved := true
 131  gap3_shear_witness_constructed := true
 132  gap3_full_tt_decomposition_open := true
 133  gap4_flat_tt_convergence_proved := true
 134  gap4_curved_qnm_open := true
 135  gap5_lattice_dirac_relations_proved := true
 136  gap5_continuum_algebra_hkt_open := true
 137  gap6_kinematical_wick_certified := true
 138  gap6_action_continuation_open := true
 139  gap7_seam_grammar_verdict_certified_miss := true
 140  gap7_true_mechanism_open := true
 141
 142/-- The campaign did not achieve (and does not claim) full physical closure:
 143every gap retains an explicit OPEN component. -/
 144theorem no_full_physical_closure_claimed :
 145    sevenGapsCampaignStatus.gap1_hessian_symbol_comparison_open = true
 146      ∧ sevenGapsCampaignStatus.gap2_continuum_limit_open = true
 147      ∧ sevenGapsCampaignStatus.gap3_full_tt_decomposition_open = true
 148      ∧ sevenGapsCampaignStatus.gap4_curved_qnm_open = true
 149      ∧ sevenGapsCampaignStatus.gap5_continuum_algebra_hkt_open = true
 150      ∧ sevenGapsCampaignStatus.gap6_action_continuation_open = true
 151      ∧ sevenGapsCampaignStatus.gap7_true_mechanism_open = true :=
 152  ⟨rfl, rfl, rfl, rfl, rfl, rfl, rfl⟩
 153
 154/-- **Anchor theorem.**  The proved flags are not free-floating booleans:
 155this theorem re-derives one load-bearing result per gap directly from the
 156imported modules, so the ledger cannot silently drift from the artifacts.
 157(Gap 7 is quarantined and anchored in `SeamGrammarVerdict` itself.) -/
 158theorem campaign_flags_anchored :
 159    -- gap 1 (sign no-go: every bridge forces nonnegative deficits)
 160    (∀ {Λ : Type} [inst : Fintype Λ] [inst2 : DecidableEq Λ]
 161      (L : RecognitionLedger.RecognitionLedger Λ) (H : Type)
 162      (b : LedgerToHingeBridge H L) (i : Λ),
 163        0 ≤ b.geometricDeficit (b.x_sigma i))
 164    -- gap 2 (count-finiteness of the scoped class)
 165    ∧ (∀ B : ℕ, 0 < Fintype.card (PathSumMeasure.BoundedComplex B))
 166    -- gap 4 (flat TT eigenvalue convergence for every fixed AXIS mode;
 167    -- axis sector only, see the gap-4 scope note in the module header)
 168    ∧ (∀ k : ℕ, Filter.Tendsto
 169        (fun N : ℕ => 4 * (N : ℝ) ^ 2 * Real.sin (Real.pi * k / N) ^ 2)
 170        Filter.atTop (nhds ((2 * Real.pi * k) ^ 2)))
 171    -- gap 5 (abelian momentum sector, n = 8 instance)
 172    ∧ (∀ (a b : ZMod 8) (x : HypersurfaceDeformation.PhaseSpace 8),
 173        HypersurfaceDeformation.bracket (HypersurfaceDeformation.Dgen a)
 174          (HypersurfaceDeformation.Dgen b) x = 0)
 175    -- gap 6 (exact non-degeneracy iff on the causal class)
 176    ∧ (∀ (ty : CausalSimplexWick.CausalTetType) (a alpha : ℝ), 0 < a →
 177        (0 < Geometry.CayleyMengerPolynomial.cm3
 178            (CausalSimplexWick.euclideanSqEdges ty a alpha)
 179          ↔ CausalSimplexWick.alphaMin ty < alpha)) := by
 180  refine ⟨?_, ?_, ?_, ?_, ?_⟩
 181  · intro Λ _ _ L H b i
 182    exact bridge_forces_nonneg_geometricDeficit L b i
 183  · exact PathSumMeasure.boundedComplex_card_pos
 184  · intro k
 185    simpa [DiscreteLichnerowicz.discreteEigenvalue] using
 186      DiscreteLichnerowicz.discreteEigenvalue_tendsto k
 187  · intro a b x
 188    exact HypersurfaceDeformation.bracket_Dgen_Dgen a b x
 189  · intro ty a alpha ha
 190    exact CausalSimplexWick.cm3_euclidean_pos_iff ty a alpha ha
 191
 192end CampaignLedger
 193end SevenGaps
 194end Gravity
 195end IndisputableMonolith
 196