Holography Landauer Calorimeter Descent Six Channel Heat Is Posted Record Flux

The six-channel heat identity

In the Recognition Science framework, a ledger is a discrete record of events, and recognition is the act of posting an event to that record. The declaration sixChannelHeat_is_posted_record_flux is a theorem in the framework's machine-checked library of formal theorems. It establishes that a quantity called heat, defined as the sum of six separate face-channel contributions, is identical to the posted record flux of a cell. The identity holds for any real scaling factor q, meaning the six-channel sum is not an approximation but an exact equality.

The proof works by construction. The framework defines a cell configuration and six face bits, each checking whether a specific set of vertices is closed. The six-channel heat is the sum of the individual Clausius one-channel heats for each face bit. A channel-aggregation theorem shows this sum equals the cell's step heat. Scaling this sum by q produces a physical step heat that satisfies the posted record flux condition. The proof is not a definitional shortcut: it does not simply declare heat to be q times the cell heat. Instead, it builds the heat from the six face channels and then proves the equality through the aggregation theorem.

The declaration also establishes uniqueness. Any heat function that satisfies the posted record flux condition must equal the tautological selector, pointwise. The six-channel construction meets this unique value. The framework also tests a decoy: a five-channel truncation that omits one face channel fails the carrier premise on a concrete posting step. This discrimination shows the six channels are not arbitrary; each contributes to the identity.

What the declaration does not claim is equally important. It does not provide an independent external calorimeter. The six-channel heat is still the ledger posting rule, lifted from one-channel atoms to a cell type. It is an aggregation of the banked posting rule, not a new physical measurement device. The framework states this residual explicitly: independent external calorimeter identification remains an open target. The theorem is a type-lift, not a physical discovery.

/-- The six-channel Clausius lift inhabits `HeatIsPostedRecordFlux` via
channel aggregation (not by defining heat as `q * stepHeatCell`). This is a
type-lift of the banked posting rule, not an independent external calorimeter. -/
theorem sixChannelHeat_is_posted_record_flux (q : ℝ) :
    HeatIsPostedRecordFlux q (sixChannelHeat q) := by
  intro c c'
  exact sixChannelHeat_eq_scaled_stepHeatCell q c c'

/-- The six-channel calorimeter equals scaled posted flux by channel
aggregation, not by definitional identification with `stepHeatCell`. -/
theorem sixChannelHeat_eq_scaled_stepHeatCell (q : ℝ) (c c' : CellCfg) :
    sixChannelHeat q c c' = q * (stepHeatCell c c' : ℝ) := by
  simp only [sixChannelHeat, stepHeatCell_eq_sum_face_channels c c']

/-- Any inhabitant of the carrier premise is pointwise the tautological
selector. The six-channel construction meets that unique value by the
aggregation theorem above. -/
theorem heat_carrier_unique (q : ℝ) (heat : PhysicalStepHeat)
    (h : HeatIsPostedRecordFlux q heat) :
    heat = tautologicalPostedHeat q := by
  funext c c'
  exact h c c'

theorem five_channel_fails_unit_carrier :
    ¬ HeatIsPostedRecordFlux 1 (fiveChannelHeat 1) := by
  intro h
  have hstep := h cell0 postingStepTarget
  have hne := five_channel_sum_ne_stepHeatCell
  simp only [fiveChannelHeat] at hstep
  exact hne (by exact_mod_cast hstep)

What this page does not claim

This declaration does not provide an independent external calorimeter. The theorem does not establish a new physical law beyond the ledger posting rule. The identity does not claim that heat is a fundamental physical quantity in conventional thermodynamics.

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/Holography/LandauerCalorimeterDescent.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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