Encyclopedia Foundation Foundation Pair Kernel Event Metric Pricing S16 Ledger Cost Energy Does Not Read

ARTICLE 5 claims 4 theorems 1 model

Foundation Pair Kernel Event Metric Pricing S16 Ledger Cost Energy Does Not Read

A formal theorem draws a precise line: the ledger's cost of energy is not the recognition price, and the difference is a target, not a failure.

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The energy readout boundary

The declaration ledgerCostEnergy_does_not_read_recognitionPrice is a theorem in the framework's machine-checked library of formal theorems. It states that a specific mathematical object, the ledger cost of an event's energy, does not equal the recognition configuration price for that event. The theorem is a negative result: it proves that one proposed way of reading energy from the framework's structure is not valid.

The theorem concerns a particular construction, ledgerCostEventKinematics3, which assigns to every posting event a constant energy equal to the value of the cost function J at 1, and a constant duration equal to the native time unit tau0. The theorem proves that this construction does not satisfy the property PostingEnergyReadsRecognitionConfigurationPrice3, which would require the energy of an event to equal the price of its parent configuration. The proof is a direct computation, with no sorry and no new axiom.

The result is best understood as a boundary marker. The framework's library separates what is mathematically forced from what remains a modeling choice. This theorem shows that the energy readout is not forced by the structure that forces the clock and the configuration dimension. The clock readout is unique, and the configuration dimension is forced to be D+2, but the energy readout is not. The theorem does not say that energy cannot be read from the configuration price; it says that the particular ledger cost construction does not do so.

The positive statement that energy does read the configuration price is a separate, explicit target. The library's docstring states that posting energy reads the recognition configuration price, but this is marked as a target, not a theorem. The theorem ledgerCostEnergy_does_not_read_recognitionPrice is the precise negative result that isolates this target. It does not claim that the target is false; it claims that the target is not established by the ledger cost construction.

THEOREM ledgerCostEnergy_does_not_read_recognitionPrice · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean
ledgerCostEnergy_does_not_read_recognitionPrice · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean:666 
theorem ledgerCostEnergy_does_not_read_recognitionPrice :
    ¬ PostingEnergyReadsRecognitionConfigurationPrice3
      canonicalChannel
      (@parentDerivedPostingConfigurationDimension3 3 _)
      (ledgerCostEventKinematics3 3) := by
  intro hread
  obtain ⟨pair, hpair⟩ :=
    realizedPrimitivePostingPair3_exists
  let event : RealizedPostingEvent3 3 :=
    ⟨pair, hpair⟩
  have h := hread event
  change
    Cost.Jlog 1 =
      recognitionConfigurationPrice canonicalChannel
        (parentDerivedPostingConfigurationDimension3 event) at h
  rw [recognitionConfigurationPrice_eq_phi_zpow_neg] at h
  rw [show
      parentDerivedPostingConfigurationDimension3 event =
        GapDerivation.configDim GapDerivation.D by
          exact
            parentDerivedConfiguration_has_forcedDimension
              event] at h
  exact ledgerJlogUnitCost_ne_constants_hbar
    (h.trans GapDerivation.hbar_exponent_eq_configDim.symm)
THEOREM ledgerCostEnergy_does_not_read_recognitionPrice · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean
ledgerCostEnergy_does_not_read_recognitionPrice · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean:666 
theorem ledgerCostEnergy_does_not_read_recognitionPrice :
    ¬ PostingEnergyReadsRecognitionConfigurationPrice3
      canonicalChannel
      (@parentDerivedPostingConfigurationDimension3 3 _)
      (ledgerCostEventKinematics3 3) := by
  intro hread
  obtain ⟨pair, hpair⟩ :=
    realizedPrimitivePostingPair3_exists
  let event : RealizedPostingEvent3 3 :=
    ⟨pair, hpair⟩
  have h := hread event
  change
    Cost.Jlog 1 =
      recognitionConfigurationPrice canonicalChannel
        (parentDerivedPostingConfigurationDimension3 event) at h
  rw [recognitionConfigurationPrice_eq_phi_zpow_neg] at h
  rw [show
      parentDerivedPostingConfigurationDimension3 event =
        GapDerivation.configDim GapDerivation.D by
          exact
            parentDerivedConfiguration_has_forcedDimension
              event] at h
  exact ledgerJlogUnitCost_ne_constants_hbar
    (h.trans GapDerivation.hbar_exponent_eq_configDim.symm)
MODEL ledgerCostEventKinematics3 · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean
ledgerCostEventKinematics3 · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean:655 
/-- Physical-energy countermodel using the actual dimensionless ledger cost.
It is positive and preserves one-tick duration, but it cannot read the forced
configuration price. -/
def ledgerCostEventKinematics3
    (N : ℕ) [NeZero N] :
    PostingEventKinematics3 N where
  energy := fun _ => Cost.Jlog 1
  duration := fun _ => Constants.tau0
  energy_pos := fun _ => ledgerJlogUnitCost_pos
  duration_pos := fun _ => Constants.tau0_pos
THEOREM ledgerCostEnergy_does_not_read_recognitionPrice · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean
ledgerCostEnergy_does_not_read_recognitionPrice · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean:666 
theorem ledgerCostEnergy_does_not_read_recognitionPrice :
    ¬ PostingEnergyReadsRecognitionConfigurationPrice3
      canonicalChannel
      (@parentDerivedPostingConfigurationDimension3 3 _)
      (ledgerCostEventKinematics3 3) := by
  intro hread
  obtain ⟨pair, hpair⟩ :=
    realizedPrimitivePostingPair3_exists
  let event : RealizedPostingEvent3 3 :=
    ⟨pair, hpair⟩
  have h := hread event
  change
    Cost.Jlog 1 =
      recognitionConfigurationPrice canonicalChannel
        (parentDerivedPostingConfigurationDimension3 event) at h
  rw [recognitionConfigurationPrice_eq_phi_zpow_neg] at h
  rw [show
      parentDerivedPostingConfigurationDimension3 event =
        GapDerivation.configDim GapDerivation.D by
          exact
            parentDerivedConfiguration_has_forcedDimension
              event] at h
  exact ledgerJlogUnitCost_ne_constants_hbar
    (h.trans GapDerivation.hbar_exponent_eq_configDim.symm)
THEOREM ledgerCostEnergy_does_not_read_recognitionPrice · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean
ledgerCostEnergy_does_not_read_recognitionPrice · IndisputableMonolith/Foundation/PairKernelEventMetricPricingS16.lean:666 
theorem ledgerCostEnergy_does_not_read_recognitionPrice :
    ¬ PostingEnergyReadsRecognitionConfigurationPrice3
      canonicalChannel
      (@parentDerivedPostingConfigurationDimension3 3 _)
      (ledgerCostEventKinematics3 3) := by
  intro hread
  obtain ⟨pair, hpair⟩ :=
    realizedPrimitivePostingPair3_exists
  let event : RealizedPostingEvent3 3 :=
    ⟨pair, hpair⟩
  have h := hread event
  change
    Cost.Jlog 1 =
      recognitionConfigurationPrice canonicalChannel
        (parentDerivedPostingConfigurationDimension3 event) at h
  rw [recognitionConfigurationPrice_eq_phi_zpow_neg] at h
  rw [show
      parentDerivedPostingConfigurationDimension3 event =
        GapDerivation.configDim GapDerivation.D by
          exact
            parentDerivedConfiguration_has_forcedDimension
              event] at h
  exact ledgerJlogUnitCost_ne_constants_hbar
    (h.trans GapDerivation.hbar_exponent_eq_configDim.symm)

What this page does not claim

The theorem does not claim that energy cannot be read from the configuration price. The theorem does not claim that the target statement is false. The theorem does not establish any property of the actual physical energy of a posting event.

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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/Foundation/PairKernelEventMetricPricingS16.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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