Foundation Pair Kernel Production Event Response Generation S24 Consumer S24 S13

A consumer that compiles

The declaration s24_S13_nonlinearGauss_tangentGreen_consumer_compiles is a definition in the framework's machine-checked library of formal statements. It states that a particular consumer, the canonical exact tangent consumer from the S13 nonlinear Gauss law layer, compiles unchanged into the S24 production event-response generation package. In plain terms: a previously established piece of the framework, which handles a nonlinear Gauss law with a tangent Hessian and Green function, remains valid and usable when the larger S24 package is assembled.

The library's S24 package is a collection of formal statements about production event-response systems. It includes a source catalog with five explicit event witnesses, a quotient structure, and a scale-covariant readout consumer. The S13 consumer is one of several components that the S24 package reuses. The declaration s24_S13_nonlinearGauss_tangentGreen_consumer_compiles simply re-exports the earlier S13 consumer declaration, which asserts the existence of a canonical exact tangent consumer. It does not add new mathematical content about the Gauss law itself; it records that the S13 result carries over without modification.

What the declaration does not claim is equally important. It does not assert that any physical system satisfies the S13 consumer's conditions. It only states that the consumer exists in the formal library. The S24 package also contains a separate statement, transportedProduction_scaleCovariant_consumer_exists, which does assert that a physical system with a transport arrow produces a realized event with normalized duration, energy, and action equal to a canonical price, and a carrier dimension of 5. That statement is conditional on the system having the transport property; the s24_S13 declaration is not about such physical existence.

The declaration also does not claim that the S13 consumer is the only consumer, nor that the S24 package closes all physical residuals. The package explicitly records that committed ancestry still admits systems that split on source-act transport. The s24_S13 definition is a bookkeeping step: it marks the S13 consumer as compiled into S24, nothing more.

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

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

/-- The complete source witness catalog and its universal property compile as
one package without selecting a physical response system. -/
theorem productionEventResponse_sourceCatalog_consumer :
    (∀ response : RecognitionParentResponse3,
      ∃ act : ProductionEventResponseAct3,
        productionEventResponseAct_read act = response) ∧
      Fintype.card ProductionEventResponseClass3 = 5 ∧
      (∀ {β : Type*}
          (map : ProductionEventResponseAct3 → β),
        ProductionEventResponseInvariantMap3 map →
          ∃! descended :
              ProductionEventResponseClass3 → β,
            ∀ act,
              descended
                  (PrimitiveRecognitionCalculus.QuotientSelection.proj
                    productionEventResponseProbeFamily3 act) =
                map act) :=
  ⟨every_response_has_productionEventAct,
    productionEventResponseClass_card_eq_five,
    productionEventResponseInvariantMap_factors_unique⟩

What this page does not claim

This declaration does not assert that any physical system satisfies the S13 consumer's conditions. It does not claim the S24 package closes all physical residuals; the package explicitly records that committed ancestry admits systems that split on source-act transport. It does not add new mathematical content about the nonlinear Gauss law itself.

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)

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.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: