Encyclopedia Foundation Foundation Pair Kernel Production Effect Physicality S26 Consumer S26 S24 Source

ARTICLE 4 claims 3 theorems 1 model

Foundation Pair Kernel Production Effect Physicality S26 Consumer S26 S24 Source

A machine-checked theorem compiles the source-level catalog of production events into a complete, five-class package that carries no physical assumptions, and proves physical readouts appear only when a separate realization arrow is supplied.

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The source catalog consumer

The declaration s26_S24_source_consumer_compiles is a definition in the framework's machine-checked library of formal theorems. It names a single package that bundles the source-level results from an earlier stage, S24, into one consumer object. The package's content is a theorem: the source catalog of production events, when quotiented by its effect classes, has exactly five classes, every operation has a probe that observes it, the coordinate representation is injective, and the quotient satisfies a universal property. That universal property says any map from operations to another type that respects the effect invariant descends uniquely through the quotient. In plain terms, the source catalog is a complete, five-class structure with no redundancy and a canonical way to map it onto any other structure that respects the same distinctions.

The definition itself compiles without any physical selection. The docstring states this explicitly: the five-class source effect quotient, its universal property, orientation, batch addition, and effect extensionality all compile without physical selection. The word "consumer" in the name marks this as the receiving end of a pipeline: it takes the S24 source catalog as input and produces the compiled package as output. The declaration is a definition, not a new theorem; its content is the theorem it references, and its role is to make that content available under a single name for later stages of the framework.

Physical readouts are a separate matter. The same source file contains a theorem, effectRealizedProduction_scaleCovariant_consumer_exists, which states that physical readouts compile only under an exact effect realization arrow. That arrow is a hypothesis: a system must satisfy ProductionEffectsRealizePhysicalChannels3 before the theorem produces a realized posting event with normalized duration, energy, action, carrier dimension five, and observability. The S24 consumer package does not supply that arrow. It establishes the source catalog as a complete algebraic structure; it does not establish that any physical system realizes it.

What the declaration does not claim is as important as what it proves. It does not claim that the five-class structure is physically instantiated, that any real production process exists, or that the source catalog alone determines any physical measurement. Those claims require the realization arrow, which is a separate hypothesis. The framework's own docstring marks this boundary: S17-S20 physical readouts compile once the exact effect-to-channel realization arrow is supplied. The S24 consumer compiles the source side; the physical side remains conditional.

The consequence for a reader is a clear separation of concerns. The source catalog is a proved algebraic object, available for any further formal work that needs a five-class quotient with a universal property. Physical claims are not part of that package; they are gated behind a named hypothesis. This is the framework's discipline: the algebraic core is unconditional, the physical bridge is conditional, and the two are never conflated in the same theorem.

MODEL s26_S24_source_consumer_compiles · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean
s26_S24_source_consumer_compiles · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean:122 
def s26_S24_source_consumer_compiles :=
  PairKernelProductionEventResponseGenerationS24Consumer.productionEventResponse_sourceCatalog_consumer
THEOREM productionEffect_source_consumer · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean
productionEffect_source_consumer · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean:40 
/-- The complete source-effect result consumed as one package. -/
theorem productionEffect_source_consumer :
    Fintype.card ProductionOperationEffectClass3 = 5 ∧
      (∀ operation : ProductionSourceOperation3,
        ∃ probe : ProductionOperationEffectProbe3,
          productionOperationEffectObservation3 probe operation = 1) ∧
      Function.Injective
        productionOperationEffectCoordinateRepresentation3 ∧
      (∀ {β : Type*}
          (map : ProductionSourceOperation3 → β),
        ProductionOperationEffectInvariantMap3 map →
          ∃! descended :
              ProductionOperationEffectClass3 → β,
            ∀ operation,
              descended
                  (productionOperationEffectClass3 operation) =
                map operation) :=
  ⟨productionOperationEffectClass_card_eq_five,
    everyProductionOperation_has_nontrivialEffect,
    productionOperationEffectCoordinateRepresentation_injective,
    productionOperationEffectInvariantMap_factors_unique⟩
THEOREM productionEffect_source_consumer · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean
productionEffect_source_consumer · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean:40 
/-- The complete source-effect result consumed as one package. -/
theorem productionEffect_source_consumer :
    Fintype.card ProductionOperationEffectClass3 = 5 ∧
      (∀ operation : ProductionSourceOperation3,
        ∃ probe : ProductionOperationEffectProbe3,
          productionOperationEffectObservation3 probe operation = 1) ∧
      Function.Injective
        productionOperationEffectCoordinateRepresentation3 ∧
      (∀ {β : Type*}
          (map : ProductionSourceOperation3 → β),
        ProductionOperationEffectInvariantMap3 map →
          ∃! descended :
              ProductionOperationEffectClass3 → β,
            ∀ operation,
              descended
                  (productionOperationEffectClass3 operation) =
                map operation) :=
  ⟨productionOperationEffectClass_card_eq_five,
    everyProductionOperation_has_nontrivialEffect,
    productionOperationEffectCoordinateRepresentation_injective,
    productionOperationEffectInvariantMap_factors_unique⟩
THEOREM effectRealizedProduction_scaleCovariant_consumer_exists · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean
effectRealizedProduction_scaleCovariant_consumer_exists · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean:62 
/-- S17-S20 physical readouts compile once the exact effect-to-channel
realization arrow is supplied. -/
theorem effectRealizedProduction_scaleCovariant_consumer_exists
    (system : PostingPhysicalResponseSystem3.{0} 3)
    (hrealize :
      ProductionEffectsRealizePhysicalChannels3 system) :
    ∃ event : RealizedPostingEvent3 3,
      normalizedPostingDuration3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            system
            ((productionOperationSelectors_iff_observableExhaustion
              system).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                system).1 hrealize)))
          event.1 = 1 ∧
        normalizedPostingEnergy3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            system
            ((productionOperationSelectors_iff_observableExhaustion
              system).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                system).1 hrealize)))
          event.1 =
            canonicalPostingEventChannelPrice3 event ∧
        normalizedPostingAction3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            system
            ((productionOperationSelectors_iff_observableExhaustion
              system).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                system).1 hrealize)))
          event.1 =
            canonicalPostingEventChannelPrice3 event ∧
        physicalPostingCarrierDimension3
          (observableProductionPhysicalChannelCarrier3
            system
            ((productionOperationSelectors_iff_observableExhaustion
              system).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                system).1 hrealize)))
          event = 5 ∧
        PostingCarrierResponseObservability3
          (observableProductionResponseSystem3
            system
            ((productionOperationSelectors_iff_observableExhaustion
              system).1
              ((productionEffectsRealizeChannels_iff_operationSelectors
                system).1 hrealize))) := by
  exact
    operationSelectedProduction_scaleCovariant_consumer_exists
      system
      ((productionEffectsRealizeChannels_iff_operationSelectors
        system).1 hrealize)

What this page does not claim

The declaration does not claim that any physical system realizes the five-class source catalog. The declaration does not claim that physical readouts exist without the separate realization arrow. The declaration does not claim that the source catalog alone determines any physical measurement.

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/PairKernelProductionEffectPhysicalityS26Consumer.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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