Holography Landauer Calorimeter Forcing Tautological Inhabits Smuggling Package

A smuggling check

The declaration tautological_inhabits_smuggling_package is a formal proof in the framework's machine-checked library of theorems. It establishes a negative result about a proposed physical law. The proposal was to define the heat posted between two states of a cell as a sum over six independent face channels, each channel contributing a fixed quantum of heat when a face flips. The theorem proves that this package of axioms, which looks like an independent physical constraint, is actually a definitional trick: it forces the heat to equal exactly the tautological heat that was already defined by the posting rule itself.

The proof works by unfolding definitions. The theorem smuggling_package_forces_carrier shows that any heat function satisfying the package must equal tautologicalPostedHeat. This is not a derivation of a new law; it is a restatement of the old one. The package smuggles the conclusion into its own assumptions. A separate theorem, smuggling_package_eq_tautological, makes the same point directly: the package is equivalent to the tautological heat. This is why the framework calls it a smuggling package rather than a forcing result.

The declaration also shows what the package does not do. It does not provide an independent calorimeter, a physical mechanism that would force the heat law from more basic principles. The framework names this missing piece explicitly as MissingIndependentCellCalorimeter. The proof weak_axioms_admit_scaled_decoy demonstrates the gap: if you drop the unit quantum requirement, a scaled version of the heat law satisfies the weaker axioms but is not the tautological heat. This scaled decoy shows that the full package is needed, and that the full package is just a definitional restatement.

In plain terms, the declaration is a warning label. It says: this particular route to deriving a heat law is circular. The framework does not claim to have derived the Landauer principle from this package. It claims only to have identified a formal trap and to have named the missing ingredient that would be needed for a genuine derivation. The stub LogicalBitResetProtocol is a sketch, not a proof, and the framework explicitly says no logical discharge is claimed.

theorem smuggling_package_forces_carrier
    (q : ℝ) (heat : PhysicalStepHeat)
    (h : SmugglingCalorimeterPackage q heat) :
    HeatIsPostedRecordFlux q heat := by
  rcases h with ⟨channel, hunit, hadd⟩
  intro c c'
  have hsum := stepHeatCell_eq_sum_faceAtom c c'
  rw [hadd, hsum, Int.cast_sum, Finset.mul_sum]
  refine Finset.sum_congr rfl ?_
  intro i _
  rw [channel_unit_eval q channel hunit i (faceBit c i) (faceBit c' i),
    faceAtom_cast]

theorem smuggling_package_eq_tautological
    (q : ℝ) (heat : PhysicalStepHeat)
    (h : SmugglingCalorimeterPackage q heat) :
    ∀ c c' : CellCfg, heat c c' = tautologicalPostedHeat q c c' := by
  intro c c'
  simpa [tautologicalPostedHeat] using
    smuggling_package_forces_carrier q heat h c c'

/-- Weak axioms (kernel silence + face additivity, no unit quantum) do not
force the unit tautological calorimeter. -/
theorem weak_axioms_admit_scaled_decoy :
    KernelSilent doublePostedHeat ∧
      FaceChannelAdditive doublePostedHeat ∧
        ¬ (∀ c c' : CellCfg,
            doublePostedHeat c c' = tautologicalPostedHeat 1 c c') :=
  ⟨doublePostedHeat_kernel_silent, doublePostedHeat_face_additive,
    doublePostedHeat_ne_unit_tautological⟩

/-- Named gap type for an independent cell calorimeter. A discharge would
supply a `PhysicalStepHeat` equal to scaled `stepHeatCell` for a reason that
does not package the six-channel posting rule into the hypothesis list.
Inhabiting this structure does not close the residual. -/
structure MissingIndependentCellCalorimeter where
  named_gap : Unit := ⟨⟩

What this page does not claim

The declaration does not prove that the Landauer principle is true. The declaration does not provide an independent derivation of the heat law. The logical reset protocol stub is not a proof of any physical claim.

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/LandauerCalorimeterForcing.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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