IndisputableMonolith.Gravity.Analysis.ReggeTTBlochConventionAudit

   1import IndisputableMonolith.Gravity.Analysis.ReggeTTBlochInterfaceAudit
   2import IndisputableMonolith.Gravity.Analysis.ReggeTTContinuumCertificateSpike
   3
   4/-!
   5# Regge TT Bloch convention sidecar, attempt 2
   6
   7This sidecar is intentionally not imported by production modules.  It imports
   8the committed spike transcription only here, as required by the panel
   9protocol.
  10
  11Attempt 2 does not prove Gate B.  The interface moment is now a stencil fold,
  12not a definition wired to the spike blocks, so the equality to
  13`tetBlock0 + ... + tetBlock5` remains an honest convention bridge target.
  14-/
  15
  16namespace IndisputableMonolith
  17namespace Gravity
  18namespace Analysis
  19namespace ReggeTTBlochConventionAudit
  20
  21open ReggeTTBlochInterfaceAudit
  22
  23noncomputable section
  24
  25/-- Scalar packet passed to the committed spike transcription. -/
  26structure SpikeInput where
  27  E00 : ℝ
  28  E01 : ℝ
  29  E02 : ℝ
  30  E10 : ℝ
  31  E11 : ℝ
  32  E12 : ℝ
  33  E20 : ℝ
  34  E21 : ℝ
  35  E22 : ℝ
  36  x0 : ℝ
  37  x1 : ℝ
  38  x2 : ℝ
  39
  40/-- Matrix/vector marshalling into the scalar language of the spike file. -/
  41def spikeInput (E : Fin 3 → Fin 3 → ℝ) (x : Fin 3 → ℝ) : SpikeInput where
  42  E00 := E 0 0
  43  E01 := E 0 1
  44  E02 := E 0 2
  45  E10 := E 1 0
  46  E11 := E 1 1
  47  E12 := E 1 2
  48  E20 := E 2 0
  49  E21 := E 2 1
  50  E22 := E 2 2
  51  x0 := x 0
  52  x1 := x 1
  53  x2 := x 2
  54
  55/-- The literal committed spike LHS, with `s2 = sqrt 2`, `s3 = sqrt 3`, and
  56`p = pi` as required by attempt 2. -/
  57def committedSpikeLHS (input : SpikeInput) : ℝ :=
  58  ReggeTTContinuumCertificateSpike.tetBlock0
  59      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
  60      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
  61      (Real.sqrt 2) (Real.sqrt 3) Real.pi
  62    + ReggeTTContinuumCertificateSpike.tetBlock1
  63      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
  64      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
  65      (Real.sqrt 2) (Real.sqrt 3) Real.pi
  66    + ReggeTTContinuumCertificateSpike.tetBlock2
  67      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
  68      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
  69      (Real.sqrt 2) (Real.sqrt 3) Real.pi
  70    + ReggeTTContinuumCertificateSpike.tetBlock3
  71      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
  72      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
  73      (Real.sqrt 2) (Real.sqrt 3) Real.pi
  74    + ReggeTTContinuumCertificateSpike.tetBlock4
  75      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
  76      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
  77      (Real.sqrt 2) (Real.sqrt 3) Real.pi
  78    + ReggeTTContinuumCertificateSpike.tetBlock5
  79      input.E00 input.E01 input.E02 input.E10 input.E11 input.E12
  80      input.E20 input.E21 input.E22 input.x0 input.x1 input.x2
  81      (Real.sqrt 2) (Real.sqrt 3) Real.pi
  82
  83/-- Gate B target proposition, left open as a definition rather than stated as
  84a theorem.  A future proof must instantiate `support`, `phaseQuadratic`, and
  85`amplitude` from the actual raw stencil and show that the moment fold matches
  86the committed spike LHS under the seven TT equations, without using
  87`tt_continuum_certificate`. -/
  88def GateBConventionTarget (support : Finset Bucket) (phaseQuadratic : Bucket → ℝ)
  89    (amplitude : Bucket → ℝ) (E : Fin 3 → Fin 3 → ℝ) (x : Fin 3 → ℝ) : Prop :=
  90  E 0 1 = E 1 0 →
  91  E 0 2 = E 2 0 →
  92  E 1 2 = E 2 1 →
  93  E 0 0 + E 1 1 + E 2 2 = 0 →
  94  x 0 * E 0 0 + x 1 * E 1 0 + x 2 * E 2 0 = 0 →
  95  x 0 * E 0 1 + x 1 * E 1 1 + x 2 * E 2 1 = 0 →
  96  x 0 * E 0 2 + x 1 * E 1 2 + x 2 * E 2 2 = 0 →
  97  reggeTTMoment support phaseQuadratic amplitude =
  98    committedSpikeLHS (spikeInput E x)
  99
 100end
 101
 102end ReggeTTBlochConventionAudit
 103end Analysis
 104end Gravity
 105end IndisputableMonolith
 106