Holography Landauer Calorimeter Descent

The six-channel heat rule

In Recognition Science, the framework that derives physics from a ledger of recognition events, heat is not a free quantity. The framework's library, a machine-checked collection of formal theorems, banks a rule: heat is whatever the ledger posts as a record flux. The construction called Landauer calorimeter descent asks what happens when that rule, stated for single atoms, is lifted to a cell with six faces. The answer, proved in the library, is that the cell's total heat is exactly the sum of the heats of its six face channels, and that this decomposition is unique.

The construction is concrete. A cell configuration is a set of eight vertices, and each of the six faces is defined by which of its four vertices are closed. For any transition between configurations, each face channel contributes a Clausius-style heat, a signed integer. The construction proves, by direct simplification, that the cell's posted flux equals the sum of these six face-channel heats. Scaling that sum by a real factor q yields a physical step heat, and the proof shows this scaled sum satisfies the same posting condition as the original. The six-channel object is not a new physical law; it is the banked posting rule expressed through the geometry of the cell.

The library also proves that this is the only way to do it. Any heat that satisfies the posting condition must equal the tautological selector, the heat defined directly as q times the cell flux. The six-channel construction meets that unique value by aggregation. To show the six channels are not redundant, the construction builds a decoy: a five-channel heat that omits one face channel. On a specific posting step, that truncated sum disagrees with the posted cell flux, and the proof shows it therefore fails the posting condition. Omitting any channel breaks the rule.

The honest residual is stated plainly in the construction itself. This is still the ledger posting rule, lifted from single atoms to cell type. It does not supply an independent external calorimeter beyond that rule. The sharper wall, that packaging unit face quantum with face additivity forces the tautological carrier, is out of scope for this aggregation construction and remains open. What the construction establishes is precise: the six face channels are the exact, minimal decomposition of the cell's posted heat, and any heat that satisfies the posting condition is the one the ledger forces.

/-- Channel aggregation: posted cell flux is exactly the sum of the six
Clausius face-channel heats. -/
theorem stepHeatCell_eq_sum_face_channels (c c' : CellCfg) :
    stepHeatCell c c' = sixChannelNativeHeat c c' := by
  unfold sixChannelNativeHeat stepHeatCell recordFlux
  rw [faceRecord_eq_faceBits c, faceRecord_eq_faceBits c', sum_fin6]
  simp [stepHeat, faceBit]
  ring

/-- 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 construction does not provide an independent external calorimeter. The six-channel rule is not a new physical law beyond the ledger posting rule. The sharper independence wall, that packaging unit face quantum with face additivity forces the tautological carrier, is not proved here.

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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