Encyclopedia Foundation Foundation Pair Kernel Executable Effect Physical Existence S27 Consumer

ARTICLE 3 claims 2 theorems 1 model

Foundation Pair Kernel Executable Effect Physical Existence S27 Consumer

A machine-checked proof that every executable effect in the Recognition Science ledger has a physical instance, closing the readout chain without an external carrier assumption.

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The S27 consumer

In Recognition Science, the ledger is a discrete record of events, and a consumer is a stage that reads from that record and produces the next level of structure. The S27 consumer is the stage where executable effects, the operations the ledger can actually run, are shown to have physical instances. The machine-checked library of formal theorems proves that for every executable S26 effect there exists a canonical event-local physical instance. That means the readout stages S17 through S20 compile without needing an external physical-carrier premise.

The main theorem, executableEffectPhysical_scaleCovariant_consumer_exists, states that there exists a realized posting event such that the normalized posting duration, energy, and action all match the canonical posting event channel price, and the physical posting carrier dimension is 5. In plain language: the scale-covariant readout consumer closes completely, with no outside argument supplying physical existence. The S13 nonlinear Gauss, tangent Hessian, and Green consumer remains unchanged.

The module also defines a chain of consumer compilation definitions, from S13 through S27, each tying a previous stage's output into the next. These definitions are not new theorems; they are the bookkeeping that shows the whole chain assembles. The effect is that the framework's account of physical existence is internal to the ledger, not imported from outside.

What changes because of this result: the framework can treat physical instances as derived from executable effects, not assumed. A reader can now see that the recognition ledger, starting from its cost function, reaches a point where physical carriers with dimension 5 appear without a separate physical postulate. That is the payoff of the S27 consumer.

THEOREM executableEffectPhysical_scaleCovariant_consumer_exists · IndisputableMonolith/Foundation/PairKernelExecutableEffectPhysicalExistenceS27Consumer.lean
executableEffectPhysical_scaleCovariant_consumer_exists · IndisputableMonolith/Foundation/PairKernelExecutableEffectPhysicalExistenceS27Consumer.lean:38 
/-- The canonical effect-generated system closes the complete scale-covariant
readout consumer with no external physical-carrier argument. -/
theorem executableEffectPhysical_scaleCovariant_consumer_exists :
    ∃ event : RealizedPostingEvent3 3,
      normalizedPostingDuration3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances)))
          event.1 = 1 ∧
        normalizedPostingEnergy3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances)))
          event.1 =
            canonicalPostingEventChannelPrice3 event ∧
        normalizedPostingAction3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances)))
          event.1 =
            canonicalPostingEventChannelPrice3 event ∧
        physicalPostingCarrierDimension3
          (observableProductionPhysicalChannelCarrier3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances)))
          event = 5 ∧
        PostingCarrierResponseObservability3
          (observableProductionResponseSystem3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances))) :=
  effectRealizedProduction_scaleCovariant_consumer_exists
    executableEffectPhysicalResponseSystem3
    executableEffects_have_physicalInstances
THEOREM executableEffectPhysical_scaleCovariant_consumer_exists · IndisputableMonolith/Foundation/PairKernelExecutableEffectPhysicalExistenceS27Consumer.lean
executableEffectPhysical_scaleCovariant_consumer_exists · IndisputableMonolith/Foundation/PairKernelExecutableEffectPhysicalExistenceS27Consumer.lean:38 
/-- The canonical effect-generated system closes the complete scale-covariant
readout consumer with no external physical-carrier argument. -/
theorem executableEffectPhysical_scaleCovariant_consumer_exists :
    ∃ event : RealizedPostingEvent3 3,
      normalizedPostingDuration3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances)))
          event.1 = 1 ∧
        normalizedPostingEnergy3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances)))
          event.1 =
            canonicalPostingEventChannelPrice3 event ∧
        normalizedPostingAction3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances)))
          event.1 =
            canonicalPostingEventChannelPrice3 event ∧
        physicalPostingCarrierDimension3
          (observableProductionPhysicalChannelCarrier3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances)))
          event = 5 ∧
        PostingCarrierResponseObservability3
          (observableProductionResponseSystem3
            executableEffectPhysicalResponseSystem3
            ((productionOperationSelectors_iff_observableExhaustion
              executableEffectPhysicalResponseSystem3).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                executableEffectPhysicalResponseSystem3).1
                  executableEffects_have_physicalInstances))) :=
  effectRealizedProduction_scaleCovariant_consumer_exists
    executableEffectPhysicalResponseSystem3
    executableEffects_have_physicalInstances
MODEL s27_S13_nonlinearGauss_tangentGreen_consumer_compiles · IndisputableMonolith/Foundation/PairKernelExecutableEffectPhysicalExistenceS27Consumer.lean
s27_S13_nonlinearGauss_tangentGreen_consumer_compiles · IndisputableMonolith/Foundation/PairKernelExecutableEffectPhysicalExistenceS27Consumer.lean:113 
def s27_S13_nonlinearGauss_tangentGreen_consumer_compiles :=
  PairKernelExactJNonlinearGaussS13Consumer.canonicalExactJTangentConsumer_exists

What this page does not claim

This module does not derive the physical carrier dimension 5 from first principles; it proves existence of an instance with that dimension. This module does not prove that all physical phenomena are ledger effects; it covers the canonical observational system described. This module does not replace the S13 consumer; that stage remains as it was.

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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/PairKernelExecutableEffectPhysicalExistenceS27Consumer.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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