IndisputableMonolith.Gravity.SevenGaps.Gap2MeasureStatusBinding

   1import IndisputableMonolith.Gravity.SevenGaps.PathSumMeasure
   2import IndisputableMonolith.Gravity.SevenGaps.ExactShellGaugePreflight
   3import IndisputableMonolith.Gravity.SevenGaps.MeasureSubstrateBlocker
   4import IndisputableMonolith.Gravity.SevenGaps.GaugeHistoryMeasure
   5import IndisputableMonolith.Gravity.SevenGaps.FullTheoryLedger
   6
   7/-!
   8# Measure-side status Bools: the Wave C1 R6 binding, and its retraction
   9
  10## History
  11
  12Wave C1 R6 flipped `pathSumMeasureStatus.substrate_measure_derived` and
  13`gaugePreflightStatus.counting_principle_derived_from_ledger` to `true` and
  14bound them to `GaugeHistoryMeasure.gap2_gauge_counting_from_history_discharged`.
  15
  16## Retraction (2026-07-26)
  17
  18Both Bools are back to `false`. The witness theorem is true, is not withdrawn,
  19and is still cited below. What is withdrawn is the reading of it as a
  20derivation of the gauge-counting principle from ledger substrate.
  21
  22The defect is stated exactly by `history_discharge_is_prior_theorem_rewritten`
  23below, which reproves the entire advertised discharge in two lines from
  24`MeasureSubstrateBlocker.gaugeOrbitMass_satisfies`, a theorem that predates the
  25history module, using nothing from that module except its own equation
  26`nuBuild E B = gaugeOrbitMass`. A statement that follows from a prior theorem
  27with the new structure erased has not been derived from the new structure.
  28
  29One caveat, because the obvious shortcut here is wrong and would reject a
  30correct derivation. The natural mechanical test is "pin the recognition data to
  31a constant and see whether the proof still runs", and the history construction
  32does fail it: `historyMeasure_is_parameter_inert` shows any two enrichments
  33give the same measure. But gauge counting has a unique solution
  34(`gaugeCountingPrinciple_iff_eq_gaugeOrbitMass`), so *every* correct derivation
  35produces exactly that measure and is output-inert in the same way. Insensitivity
  36of the output is therefore not the defect and must not be used as the gate. The
  37defect is that no new premise enters the proof. Recorded here because a gate
  38the true mechanism cannot pass is a malformed gate.
  39
  40The failure is semantic rather than syntactic circularity. `Aut` never appears
  41in `nuBuild`; the same relabeling groupoid is reimported through an equivalent
  42wrapper. That is why a name-level check would not have caught it, and why the
  43retracted claim survived a critic pass.
  44
  45The open obligation is unchanged from before Wave C1 R6: derive
  46`MeasureSubstrateBlocker.GaugeCountingPrinciple` from substrate structure
  47strictly richer than counting. It is tracked as
  48`FullTheoryLedger.fullTheoryBenchmarks.gap2_measure_derived`, which flipped to
  49`true` on 2026-07-30 via the C4/C17 assembly in `Gap2MeasureDerivation`
  50(gatekeeper-signed) — a route disjoint from the history wrapper this module
  51retracts, so the retraction stands unchanged.
  52
  53## What this module now certifies
  54
  55* Both status Bools are `false`, matching the R6 retraction.
  56* The R6 witness theorem still holds, and carries no ledger information.
  57* The gap2 roll-up flag and the continuum Bool are `false`, as before.
  58-/
  59
  60namespace IndisputableMonolith
  61namespace Gravity
  62namespace SevenGaps
  63namespace Gap2MeasureStatusBinding
  64
  65open PathSumMeasure
  66open ExactShellGaugePreflight
  67open MeasureSubstrateBlocker
  68open GaugeHistoryMeasure
  69open FullTheoryLedger
  70
  71noncomputable section
  72
  73/-- The history construction is inert in its enrichment parameter: any two
  74enrichments give the same measure. Recorded, but explicitly NOT the defect;
  75see the caveat in the module header. Uniqueness of the gauge-counting solution
  76forces every correct derivation to be inert in exactly this way. -/
  77theorem historyMeasure_is_parameter_inert
  78    (E E' : GaugeHistoryEnrichment) (B : ℕ) :
  79    nuBuild E B = nuBuild E' B :=
  80  (gap2_gauge_counting_from_history_discharged.2 E B).trans
  81    (gap2_gauge_counting_from_history_discharged.2 E' B).symm
  82
  83/-- **THE DEFECT CERTIFICATE (2026-07-26).** The advertised discharge is a
  84two-line consequence of `gaugeOrbitMass_satisfies`, which was proved before the
  85history module existed, plus that module's own equation identifying its
  86construction with `gaugeOrbitMass`. No posting, no dual-entry column, no ledger
  87state, and no enrichment is used. This is what it means to say the derivation
  88is laundered: the conclusion is old and the new structure is decorative. -/
  89theorem history_discharge_is_prior_theorem_rewritten
  90    (E : GaugeHistoryEnrichment) (B : ℕ) :
  91    GaugeCountingPrinciple (nuBuild E B) := by
  92  rw [gap2_gauge_counting_from_history_discharged.2 E B]
  93  exact gaugeOrbitMass_satisfies
  94
  95/-- **DEFECT CERTIFICATE (2026-07-26).** The counted carrier is the plain
  96carrier. Re-exported from the construction's own equivalence, so this is the
  97author's proof read against the author's claim. -/
  98theorem historyCarrier_equiv_plainCarrier (B : ℕ) :
  99    Nonempty (CanonicalHistory B ≃ PathSumMeasure.BoundedComplex B) :=
 100  ⟨CanonicalHistory.equivUnderlying⟩
 101
 102/-- **DEFECT CERTIFICATE (2026-07-26).** The construction returns the
 103pre-existing orbit mass, for every enrichment and every cap. Together with
 104inertness and the carrier equivalence this is the whole content: a true
 105presentation theorem about an object that was already defined. -/
 106theorem historyMeasure_is_the_old_measure
 107    (E : GaugeHistoryEnrichment) (B : ℕ) :
 108    nuBuild E B = gaugeOrbitMass :=
 109  gap2_gauge_counting_from_history_discharged.2 E B
 110
 111/-- **HEADLINE (retraction, 2026-07-26; flag conjuncts dropped 2026-07-30/31).**
 112The two measure-side status Bools are `false`; the R6 witness theorem still
 113holds and is not withdrawn; it is a rewriting of a prior theorem. The
 114`gap2_measure_derived = false` conjunct was dropped on 2026-07-30 when that
 115flag flipped via the C4/C17 assembly in `Gap2MeasureDerivation`
 116(gatekeeper-signed), and the `gap2_continuum_and_measure = false` conjunct on
 1172026-07-31 when the roll-up flipped with flag 9 (Jon's criterion ruling,
 118`Gap2GaugeTransport`): both routes are disjoint from the R6 history wrapper
 119this retraction concerns. -/
 120theorem gap2_measure_status_retracted :
 121    pathSumMeasureStatus.substrate_measure_derived = false ∧
 122      gaugePreflightStatus.counting_principle_derived_from_ledger = false ∧
 123        ((∀ (E : GaugeHistoryEnrichment) (B : ℕ),
 124            GaugeCountingPrinciple (nuBuild E B)) ∧
 125          (∀ (E : GaugeHistoryEnrichment) (B : ℕ),
 126            nuBuild E B = gaugeOrbitMass)) ∧
 127          (∀ (E : GaugeHistoryEnrichment) (B : ℕ),
 128            nuBuild E B = gaugeOrbitMass ∧
 129              GaugeCountingPrinciple (gaugeOrbitMass :
 130                PathSumMeasure.TriangulationClass B → ℝ)) :=
 131  ⟨rfl, rfl, gap2_gauge_counting_from_history_discharged,
 132    fun E B => ⟨historyMeasure_is_the_old_measure E B, gaugeOrbitMass_satisfies⟩⟩
 133
 134/-- Continuum status on the path-sum ledger remains open. -/
 135theorem continuum_limit_still_open :
 136    pathSumMeasureStatus.continuum_limit_derived = false :=
 137  rfl
 138
 139/-- The gap2 roll-up flag was never flipped by the R6 binding or its
 140retraction; it flipped on 2026-07-31 with flag 9 (`Gap2GaugeTransport`,
 141Jon's criterion ruling). -/
 142theorem gap2_rollup_closed_after_flag9 :
 143    fullTheoryBenchmarks.gap2_continuum_and_measure = true :=
 144  rfl
 145
 146#print axioms historyMeasure_is_parameter_inert
 147#print axioms history_discharge_is_prior_theorem_rewritten
 148#print axioms gap2_measure_status_retracted
 149
 150end
 151
 152end Gap2MeasureStatusBinding
 153end SevenGaps
 154end Gravity
 155end IndisputableMonolith
 156