Foundation Pair Kernel Physical Readout Selection S17 Physical Energy Readout Im

Physical energy readout

In Recognition Science, a physical energy readout is a definitional choice about how a measured energy value is assigned to an event. The framework models a physical event as carrying a recognition configuration, a discrete record of what the event recognized and how. A physical energy readout is then a rule that assigns a real number to each event, and the framework defines one specific kind of readout: the energy is read from a price associated with the event's recognition channel. The price itself is a function of the channel and the dimension of the event's carrier, the set of possible degrees the event can be classified into.

The declaration physicalEnergyReadout_implies_coherenceEnergy establishes a theorem about this definition. It proves that if a physical energy readout is of this price-reading kind, then the energy values it produces are exactly the coherence energy values of the framework's canonical kinematics. In plain terms: a readout that follows the price rule is forced to agree with the framework's own energy assignment. The theorem is a formal consequence of the definitions, proved in the machine-checked library of formal theorems, and it does not depend on any additional assumptions about how events act or interact.

The declaration also establishes what does not follow from the price rule. The theorem ledgerCostEnergy_not_physicalReadout proves that the framework's ledger cost energy, a different energy assignment, does not read the recognition price. And doubledEnergy_not_physicalEventEnergy proves that a readout which simply doubles the canonical energy is not a physical event energy under the definition. These counterexamples sharpen the theorem: the price rule is not vacuous, and it selects a specific energy assignment among many possible ones.

What the declaration does not claim is equally important. It does not claim that any actual physical measurement in the world is of this price-reading kind. The canonical instances in the module are MODEL witnesses, meaning they are definitional examples, not claims about which readout nature uses. Current Recognition dynamics do not select them. The theorem also does not claim that the price rule is the only way to define a physical energy readout; it proves a consequence of one definition, not a uniqueness result. And it does not claim anything about the units of the energy values, since exact-J field units are not mentioned in the module.

The consequence of the theorem is that the framework can reason about physical energy readouts in a precise, formal way. If a readout is of the price-reading kind, then its values are fixed by the framework's structure, and the theorem provides a checkable condition for when a proposed readout is or is not of that kind. This gives a formal handle on a physical concept, and it leaves open the empirical question of which readout, if any, corresponds to measurements in the laboratory.

theorem canonicalPhysicalPostingReadouts_model :
    PhysicalPostingReadoutSemantics3
      (parentPhysicalChannelCarrier3 3)
      (@canonicalPostingRecognitionChannels3 3 _)
      (@canonicalPostingEventChannelPrice3 3 _)
      (canonicalCoherenceKinematics3 3) := by
  refine
    ⟨?_,
      parentPhysicalChannelCarrier_is_complete,
      canonicalPostingRecognitionChannel_applies,
      ?_⟩
  · exact
      (canonicalMetricPricingSemantics_model
        (N := 3)).2.1
  · intro event
    change
      Constants.E_coh =
        recognitionConfigurationPrice canonicalChannel
          (physicalPostingCarrierDimension3
            (parentPhysicalChannelCarrier3 3) event)
    rw [recognitionConfigurationPrice_eq_phi_zpow_neg]
    rw [completeCarrier_dimension_eq_configDim
      parentPhysicalChannelCarrier_is_complete event]
    exact GapDerivation.Constants_E_coh_eq_configDim

theorem ledgerCostEnergy_not_physicalReadout :
    ¬ PostingEnergyReadsRecognitionConfigurationPrice3
      canonicalChannel
      (@parentDerivedPostingConfigurationDimension3 3 _)
      (ledgerCostEventKinematics3 3) :=
  ledgerCostEnergy_does_not_read_recognitionPrice

theorem doubledEnergy_not_physicalEventEnergy :
    ¬ RealizedPostingCarriesCoherenceEnergy3
      (doubledEnergyKinematics3 3) :=
  doubledEnergy_countermodel.2.1

What this page does not claim

The theorem does not claim that any actual physical measurement is of the price-reading kind. The theorem does not claim that the price rule is the only way to define a physical energy readout. The theorem does not claim anything about the units of the energy values.

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/Foundation/PairKernelPhysicalReadoutSelectionS17.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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