Foundation Pair Kernel Production Event Response Generation S24 Consumer Transpo

The transport guarantee

A transport condition is a promise that every abstract event in a source catalog can be carried over to a physical system's own events. The declaration transportedProduction_scaleCovariant_consumer_exists proves a conditional statement: if a physical system satisfies that promise, then the system admits a complete set of production observables. These observables include a normalized duration, energy, and action, each of which comes out equal to 1 or to the system's canonical channel price. The theorem also fixes the carrier dimension at 5 and requires that the resulting response system be observable.

The proof is constructive in a precise sense. It builds the observables from the transport arrow itself, using an equivalence that ties the transport promise to a condition called observable exhaustion. That equivalence is part of the same theorem package. The result is a scale-covariant consumer, meaning the observables transform consistently when the system's scale changes. The declaration is tagged THEOREM in the framework's machine-checked library of formal theorems, with no framework-specific axioms beyond the standard three logical postulates.

What the declaration does not claim is just as important. It does not assert that every physical system satisfies the transport promise. It only says that if the promise holds, the observables exist. The framework's own notes flag a residual: committed ancestry still admits systems that split on source-act transport, so the transport condition is not automatically satisfied. The theorem also does not identify which physical systems meet the promise; that identification remains a separate question. Finally, the declaration says nothing about the numerical values of the observables beyond the normalization and price equalities; it establishes existence and structure, not specific magnitudes.

The practical upshot is a clean interface. A candidate physical system that compiles through the transport arrow gets a full set of production observables for free, with the carrier dimension and observability conditions baked in. A system that fails the transport promise gets no such guarantee from this theorem. The framework leaves that gap open on purpose, as a defined target rather than a hidden assumption.

/-- Once the source-to-physical transport arrow is supplied, S23 compiles the
S17-S20 scale-covariant readout consumer over the candidate system's
observational carrier. -/
theorem transportedProduction_scaleCovariant_consumer_exists
    (system : PostingPhysicalResponseSystem3.{0} 3)
    (htransport :
      ProductionTransportsEveryEventResponseAct3 system) :
    ∃ event : RealizedPostingEvent3 3,
      normalizedPostingDuration3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            system
            ((productionTransportsEveryAct_iff_observableExhaustion
              system).1 htransport))
          event.1 = 1 ∧
        normalizedPostingEnergy3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            system
            ((productionTransportsEveryAct_iff_observableExhaustion
              system).1 htransport))
          event.1 =
            canonicalPostingEventChannelPrice3 event ∧
        normalizedPostingAction3
          (observableProductionScaleCovariantPostingReadoutSemantics3
            system
            ((productionTransportsEveryAct_iff_observableExhaustion
              system).1 htransport))
          event.1 =
            canonicalPostingEventChannelPrice3 event ∧
        physicalPostingCarrierDimension3
          (observableProductionPhysicalChannelCarrier3
            system
            ((productionTransportsEveryAct_iff_observableExhaustion
              system).1 htransport))
          event = 5 ∧
        PostingCarrierResponseObservability3
          (observableProductionResponseSystem3
            system
            ((productionTransportsEveryAct_iff_observableExhaustion
              system).1 htransport)) :=
  observableProduction_scaleCovariant_consumer_exists
    system
    ((productionTransportsEveryAct_iff_observableExhaustion
      system).1 htransport)

/-- The physical residual is not silently closed: committed ancestry still
admits systems that split on source-act transport. -/
def s24_eventActTransport_independence_compiles :=
  committed_ancestry_admits_eventActTransport_split

/-- S13 nonlinear Gauss law, tangent Hessian, and Green consumer compile
unchanged. -/
def s24_S13_nonlinearGauss_tangentGreen_consumer_compiles :=
  PairKernelExactJNonlinearGaussS13Consumer.canonicalExactJTangentConsumer_exists

/-- S20 scale-covariant parent MODEL compiles unchanged. -/
def s24_S20_scale_consumer_compiles :=
  PairKernelScaleCovariantObservablesS20Consumer.canonicalScaleCovariantConsumer_exists

What this page does not claim

The theorem does not prove that any particular physical system satisfies the transport promise. The theorem does not determine numerical values for the observables beyond normalization and price equalities. The theorem does not close the residual gap where committed ancestry admits systems that split on source-act transport.

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/PairKernelProductionEventResponseGenerationS24Consumer.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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