Encyclopedia Gravity Gravity Record Flux Boost Heat Uniform Probe Attachment

ARTICLE 4 claims 3 theorems 1 model

Gravity Record Flux Boost Heat Uniform Probe Attachment

A formal bridge in Recognition Science ties a record's posted heat to a null stress flux, but only under an explicit geometric assumption.

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The uniform probe attachment

In the Recognition Science framework, a ledger (a discrete record of recognition events) assigns real weights to channels that cut across a local horizon. The declaration UniformProbeAttachment states a simple condition: every active channel covector has the same pairing q with one chosen probe vector k. In plain terms, all channels agree on how strongly they respond to a single test direction.

The framework's machine-checked library of formal theorems then proves a clean algebraic consequence. If that uniform attachment holds, the null contraction of the event-stress matrix equals q squared times the posted heat, the sum of the channel weights. With an explicit calibration law, the calibrated posted heat equals minus surface gravity times boost moment times that null stress flux. The equality is a theorem, but its two inputs, the channel covectors and the calibration, are named modeling choices, not derived facts.

A companion theorem guards against a trivial failure: if all channel covectors are zero, the stress flux vanishes and cannot represent a nonzero calibrated posted heat. The declaration itself does not claim that real recognition geometry produces uniform attachment. That derivation remains open.

MODEL UniformProbeAttachment · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean
UniformProbeAttachment · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean:31 
/--
Uniform attachment of the cut channels to one probe.  The common pairing is
an explicit geometric MODEL input; it is not inferred from the cut record.
-/
def UniformProbeAttachment
    {a s : ℕ}
    (p : ExteriorCutChannel a s → Fin 4 → ℝ)
    (k : Fin 4 → ℝ)
    (q : ℝ) : Prop :=
  ∀ ch, (∑ μ, p ch μ * k μ) = q
THEOREM quadContr_cutEventStress_eq_sq_mul_heat · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean
quadContr_cutEventStress_eq_sq_mul_heat · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean:55 
/--
Uniform probe pairing converts the fixed event-stress contraction into the
posted cut heat times the common squared pairing.
-/
theorem quadContr_cutEventStress_eq_sq_mul_heat
    {a s b r : ℕ} {kappa : ℝ}
    {H : LocalHorizonContext a s b r kappa}
    (c c' : LocalCut H)
    (p : ExteriorCutChannel a s → Fin 4 → ℝ)
    (k : Fin 4 → ℝ)
    (q : ℝ)
    (hattach : UniformProbeAttachment p k q) :
    quadContr (cutEventStress c c' p) k =
      q ^ 2 * (exteriorStepHeat c c' : ℝ) := by
  rw [quadContr_cutEventStress]
  unfold UniformProbeAttachment at hattach
  simp_rw [hattach]
  rw [← Finset.sum_mul]
  rw [← exteriorStepHeat_cast_eq_sum_channelDelta c c']
  ring
THEOREM matchesPostedBoostHeat_of_attachment · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean
matchesPostedBoostHeat_of_attachment · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean:85 
/--
With uniform channel attachment and the explicit calibration, calibrated
posted heat equals minus surface gravity times boost moment times null stress
flux.  The theorem derives the equality from two separately named inputs.
-/
theorem matchesPostedBoostHeat_of_attachment
    {a s b r : ℕ} {kappa : ℝ}
    {H : LocalHorizonContext a s b r kappa}
    (c c' : LocalCut H)
    (p : ExteriorCutChannel a s → Fin 4 → ℝ)
    (k : Fin 4 → ℝ)
    (q surfaceGravity boostMoment heatScale : ℝ)
    (hattach : UniformProbeAttachment p k q)
    (hcal : PostedBoostHeatNormalizationAssumption
      surfaceGravity boostMoment heatScale q) :
    heatScale * (exteriorStepHeat c c' : ℝ) =
      -surfaceGravity * boostMoment *
        quadContr (cutEventStress c c' p) k := by
  rw [quadContr_cutEventStress_eq_sq_mul_heat c c' p k q hattach]
  unfold PostedBoostHeatNormalizationAssumption at hcal
  rw [hcal]
  ring
THEOREM zero_covectors_fail_nonzero_posted_heat · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean
zero_covectors_fail_nonzero_posted_heat · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean:108 
/--
Load-bearing decoy: zero channel covectors produce zero stress flux, so they
cannot represent a nonzero calibrated posted heat.
-/
theorem zero_covectors_fail_nonzero_posted_heat
    {a s b r : ℕ} {kappa : ℝ}
    {H : LocalHorizonContext a s b r kappa}
    (c c' : LocalCut H)
    (k : Fin 4 → ℝ)
    (surfaceGravity boostMoment heatScale : ℝ)
    (hheat : heatScale * (exteriorStepHeat c c' : ℝ) ≠ 0) :
    ¬ heatScale * (exteriorStepHeat c c' : ℝ) =
      -surfaceGravity * boostMoment *
        quadContr
          (cutEventStress c c' (fun _ _ => (0 : ℝ))) k := by
  intro h
  rw [cutEventStress_zero_of_covector_zero] at h
  have hz :
      quadContr (0 : Matrix (Fin 4) (Fin 4) ℝ) k = 0 := by
    simp [quadContr]
  rw [hz, mul_zero] at h
  exact hheat h

What this page does not claim

UniformProbeAttachment does not assert that real recognition geometry produces uniform attachment. The declaration does not derive the channel covectors or the calibration from the cut record. The theorem does not claim that the posted heat is a physical temperature without the named normalization.

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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/RecordFluxBoostHeat.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.

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