Encyclopedia Gravity Gravity Record Flux Boost Heat

ARTICLE 4 claims 3 theorems 1 model

Gravity Record Flux Boost Heat

A machine-checked proof shows that heat posted to a recognition ledger equals a contraction of its stress, under two explicit model choices.

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The heat bridge

Gravity record flux boost heat is the name for a specific algebraic bridge in Recognition Science. It connects the heat that a recognition process posts to its ledger, a discrete record of events, to the null contraction of the same process's event-stress matrix. The bridge is not a physical law by itself; it is a proved equality between two mathematical objects, and it holds only when two named model inputs are supplied.

The first input is a uniform attachment. Each active channel covector must have the same pairing q with one fixed probe vector k. Under that condition, the framework's library proves that the stress contraction equals q² times the posted heat. The second input is a calibration law. It sets the heat scale to minus the surface gravity times the boost moment times q². With both inputs in place, a theorem derives the local boost-heat equation: calibrated posted heat equals minus surface gravity times boost moment times null stress flux.

The module also proves a decoy result. If all channel covectors are zero, the stress flux is zero, so it cannot represent a nonzero calibrated posted heat. This rules out a trivial failure mode. The theorems are checked in a machine-checked library of formal theorems, and the model inputs, the channel covectors, the probe, and the calibration are explicitly not derived from the recognition geometry. Deriving those inputs from recognition geometry remains open.

In plain language, the module shows that if you assume a uniform probe and a calibration, then the heat a recognition cut posts is exactly the null stress flux scaled by gravity and boost. The value is in the precision: the equality is proved, and the assumptions are named.

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
MODEL UniformProbeAttachment · PostedBoostHeatNormalizationAssumption · 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
PostedBoostHeatNormalizationAssumption · IndisputableMonolith/Gravity/RecordFluxBoostHeat.lean:76 
/--
Named MODEL normalization assumption required to convert bit-valued posted
heat into the local boost-energy normalization.  It supplies the whole
physical heat-scale conversion and is not derived from the record data.
-/
def PostedBoostHeatNormalizationAssumption
    (surfaceGravity boostMoment heatScale q : ℝ) : Prop :=
  heatScale = -surfaceGravity * boostMoment * q ^ 2

What this page does not claim

No claim that the model inputs, the uniform attachment or the calibration, are derived from recognition geometry. No claim that this module proves a physical law of gravity; it proves an algebraic equality under named assumptions. No claim that the heat scale conversion is unique or forced by the record data.

Verify this page

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.

Derived articles

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