IndisputableMonolith.Gravity.SevenGaps.Gap2LedgerCohomologyHostileProbe

   1/-
   2Hostile probe for Gap2LedgerCohomology (C18). Uncommitted. Read-only of production.
   3Checks: key theorems are inhabitations the kernel accepts; flag unmoved;
   4measured dims match the claimed 3/4/4 vs 3; no sorry in the production module
   5is re-checked by forcing the verdict package.
   6-/
   7import IndisputableMonolith.Gravity.SevenGaps.Gap2LedgerCohomology
   8
   9namespace IndisputableMonolith
  10namespace Gravity
  11namespace SevenGaps
  12namespace Gap2LedgerCohomologyHostileProbe
  13
  14open Gap2LedgerCohomology Gap2SizeBlindnessReach Gap2PostingCostDerivation
  15open Gap2LetterCostDichotomy Gap2GaugeVolume Gap2GluingDerivation
  16
  17noncomputable section
  18
  19/-- Probe: genuine-class package is inhabited. -/
  20theorem probe_incidence_genuine :
  21    Equivariant (incidenceCost (1 : ℝ))
  22      ∧ ¬ IsLedgerCoboundary (incidenceCost (1 : ℝ))
  23      ∧ ¬ IsCountLinear (incidenceCost (1 : ℝ))
  24      ∧ historyCost (incidenceCost (1 : ℝ)) 2 twoLoops = 0
  25      ∧ historyCost (incidenceCost (1 : ℝ)) 2 twoBridges = 2 :=
  26  ⟨(incidence_is_genuine_H1_class).1,
  27    (incidence_is_genuine_H1_class).2.2.1,
  28    (incidence_is_genuine_H1_class).2.2.2.1,
  29    (incidence_is_genuine_H1_class).2.2.2.2.1,
  30    (incidence_is_genuine_H1_class).2.2.2.2.2.1⟩
  31
  32/-- Probe: A1.7 escape decomposes as count rates (1, 0, -1/24). -/
  33theorem probe_a17_count_decomp :
  34    IsCountLinear (kindRateCost 1 0 (-(1 / 24)))
  35      ∧ KindRates (kindRateCost 1 0 (-(1 / 24))) 1 0 (-(1 / 24))
  36      ∧ ¬ IsLedgerCoboundary (kindRateCost 1 0 (-(1 / 24))) :=
  37  ⟨(a17_escape_is_count_combination).1,
  38    (a17_escape_is_count_combination).2.2.2.2,
  39    (a17_escape_is_count_combination).2.2.1⟩
  40
  41/-- Probe: measured dims 3/4/4 vs count span 3, and flag unmoved. -/
  42theorem probe_measured_and_flag :
  43    measuredH1Dim 1 = 3 ∧ measuredH1Dim 2 = 4 ∧ measuredH1Dim 3 = 4
  44      ∧ measuredCountSpanDim 2 = 3 ∧ measuredCountSpanDim 2 < measuredH1Dim 2
  45      ∧ ledgerCohomologyVerdict.measure_flag_moved = false :=
  46  ⟨rfl, rfl, rfl, rfl, measured_H1_exceeds_count_at_cap2,
  47    Gap2LedgerCohomology.index_flag_unmoved⟩
  48
  49/-- Probe: centered fibre is a coboundary; count span rank three. -/
  50theorem probe_coboundary_and_rank :
  51    IsLedgerCoboundary (centeredIncidenceCost (1 : ℝ))
  52      ∧ (∀ cV cE cT : ℝ,
  53          historyCost (kindRateCost cV cE cT) 1 (dust 1) = 0 →
  54          historyCost (kindRateCost cV cE cT) 2 (bouquet 1 0) = 0 →
  55          historyCost (kindRateCost cV cE cT) 2 (bouquet 0 1) = 0 →
  56          cV = 0 ∧ cE = 0 ∧ cT = 0) :=
  57  ⟨centeredIncidence_is_coboundary 1, count_span_rank_three⟩
  58
  59/-- Witness sizes match the (2,2,0) obstruction pair. -/
  60theorem probe_witness_counts :
  61    twoLoops.nV = 2 ∧ twoLoops.nE = 2 ∧ twoLoops.nT = 0
  62      ∧ twoBridges.nV = 2 ∧ twoBridges.nE = 2 ∧ twoBridges.nT = 0
  63      ∧ properEdgeCount twoLoops = 0 ∧ properEdgeCount twoBridges = 2 := by
  64  refine ⟨rfl, rfl, rfl, rfl, rfl, rfl, ?_, ?_⟩
  65  · exact properEdgeCount_twoLoops
  66  · exact properEdgeCount_twoBridges
  67
  68end
  69
  70#print axioms probe_incidence_genuine
  71#print axioms probe_a17_count_decomp
  72#print axioms probe_measured_and_flag
  73#print axioms probe_coboundary_and_rank
  74#print axioms probe_witness_counts
  75
  76end Gap2LedgerCohomologyHostileProbe
  77end SevenGaps
  78end Gravity
  79end IndisputableMonolith
  80