Foundation Pair Kernel Physical Readout Selection S17 Physical Energy Readout Ba

Batch energy readout

The declaration physicalEnergyReadout_batchEnergy_quantized is a theorem in the Recognition Science framework's machine-checked library of formal theorems. It states that if a physical energy readout is derived from a recognition channel price, then the total energy of any finite batch of events is quantized: it can only take values that are integer multiples of a fixed, smallest unit. This is a structural consequence of the framework's definitions, not an assumption added for this result.

In the framework, a recognition is an event that the universe's ledger records, and a cost is the forced price of that recognition. The relevant definitions here model how a physical system might read out energy from such a ledger. The theorem proves that if this readout is exact, the batch energy must be a sum of individual event energies, each of which is itself a multiple of a fundamental quantum. This is the framework's analogue of the familiar fact that energy in quantum mechanics comes in discrete packets.

The theorem is a formal consequence of the framework's axioms, which include no new postulates beyond the standard ones of the ambient type theory. It is not a claim about any specific physical system, nor does it identify the numerical value of the energy quantum. The framework's current dynamics do not select which physical readout is the correct one; the theorem only constrains what any such readout must look like.

The practical upshot is a sharp consistency condition: any proposed physical energy readout that does not yield quantized batch energies is ruled out by the framework. This gives a concrete test for future models. The theorem does not, however, say that quantization is unique, nor does it determine the size of the quantum, and it does not connect the quantum to any measured constant.

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

/-- Final physical energy readout, kept separate from channel applicability. -/
def PostingEnergyReadsEventChannelPrice3
    {N : ℕ} [NeZero N]
    (price : PostingEventChannelPrice3 N)
    (kinematics : PostingEventKinematics3 N) : Prop :=
  ∀ event : RealizedPostingEvent3 N,
    kinematics.energy event.1 = price event

/-- Sum of physical event energies, independent of duration and action. -/
def postingBatchEnergy3
    {N : ℕ} [NeZero N]
    (kinematics : PostingEventKinematics3 N)
    (events : Finset (PostingPair3 N)) : ℝ :=
  ∑ event ∈ events, kinematics.energy event

What this page does not claim

The theorem does not identify the numerical value of the energy quantum. The theorem does not say which physical readout is the correct one. The theorem does not claim that quantization is unique to this framework.

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)

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