Encyclopedia Foundation Foundation Pair Kernel Executable Effect Physical Existence S27 Consumer S27 S23

ARTICLE 3 claims 3 theorems

Foundation Pair Kernel Executable Effect Physical Existence S27 Consumer S27 S23

A machine-checked library proves that certain abstract production rules automatically have a concrete physical instance, without needing an outside assumption.

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The compiled production consumer

The declaration s27_S23_production_consumer_compiles is a definition in the framework's machine-checked library of formal theorems. It packages a proof that a specific step in a long chain, called S23, works: the step that takes abstract production effects and shows they correspond to observable, physical events. The name "consumer" means this step consumes the output of earlier steps in the chain, and "compiles" means the step is fully realized, not just sketched.

In plain terms, the declaration establishes that for every executable effect in the framework's system, there exists a canonical physical event that realizes it. The proof, named executableEffectPhysical_scaleCovariant_consumer_exists, shows this event has the correct normalized duration, energy, and action, and that it lives in a space of dimension 5. The declaration also confirms that the full chain of earlier steps, from S13 through S26, all compile together for this canonical system.

What this does not claim is broader physical significance. It does not say the framework has discovered a new law of nature, nor that this proof applies to systems outside the framework's own definitions. The proof is about the framework's internal consistency: its abstract production rules have a concrete physical model within its own system. It does not claim that this model matches any particular experiment or measurement.

The practical consequence is that the framework can proceed without an external physical-carrier argument. The proof closes a gap: the readouts from earlier steps no longer need an outside assumption to be physically meaningful. This is a step toward the framework's larger goal of deriving physical structure from its foundational principles, but it is a step about internal coherence, not a claim about the external world.

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
THEOREM s27_S13_nonlinearGauss_tangentGreen_consumer_compiles · s27_S26_effect_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
s27_S26_effect_consumer_compiles · IndisputableMonolith/Foundation/PairKernelExecutableEffectPhysicalExistenceS27Consumer.lean:95 
def s27_S26_effect_consumer_compiles :=
  productionEffect_source_consumer

What this page does not claim

The declaration does not claim the proof applies to any physical system outside the framework's own definitions. The declaration does not claim the framework's canonical physical model matches any measured experimental value. The declaration does not claim the framework has derived a new law of nature.

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/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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