Encyclopedia Foundation Foundation Pair Kernel Production Effect Physicality S26 Consumer S26 Effect Rea

ARTICLE 4 claims 2 theorems 2 models

Foundation Pair Kernel Production Effect Physicality S26 Consumer S26 Effect Rea

A machine-checked declaration confirms that a five-class production-effect structure compiles independently of physical realization, and that physical readouts appear only when a specific realization arrow is supplied.

Verify this page

The independence compilation

The declaration s26_effectRealization_independence_compiles is a formal definition in the framework's machine-checked library of formal theorems. It states, in effect, that the five-class source-effect quotient compiles without physical selection. The declaration is an alias for a split that separates the purely combinatorial structure of production effects from any physical interpretation. The five classes, the universal property, the orientation, batch addition, and effect extensionality all compile without needing a physical channel. This is the independence part of the name.

The physical part is separate. Physical readouts, such as duration, energy, action, and carrier dimension, compile only under the exact effect realization arrow. The declaration shows that this arrow is equivalent to S25 selectors, S24 transport, and S23 exhaustion. In plain language, the framework can describe a production effect as a pure structure, and only when a specific mapping from effects to physical channels is supplied do the physical quantities become available. The theorem productionEffect_source_consumer shows the five-class quotient with its universal property: for any map from operations to a target type that respects the invariant, there is a unique descended map from the quotient class. This is the standard universal property of a quotient.

The key theorem effectRealizedProduction_scaleCovariant_consumer_exists states that once the realization arrow is supplied, an event exists with normalized duration equal to 1, normalized energy equal to the canonical channel price, normalized action equal to that same price, and a physical carrier dimension of 5. The dimension 5 is the framework's derived spatial dimension from the forcing chain. The theorem also asserts that the response system is observable. This is the payoff of supplying the arrow: the abstract structure becomes a physical system with measurable quantities.

The declaration does not claim that physical realization is automatic. It does not claim that the five-class structure itself has physical meaning without the arrow. It does not claim that the dimension 5 is derived here; that derivation lives elsewhere in the framework. The independence is precisely that the combinatorial structure stands alone, and the physical interpretation is a separate, conditional step. The compilation check is a consistency guarantee, not a physical law.

MODEL s26_effectRealization_independence_compiles · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean
s26_effectRealization_independence_compiles · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean:116 
def s26_effectRealization_independence_compiles :=
  committedEffects_admit_physicalRealization_split
MODEL s26_effectRealization_independence_compiles · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean
s26_effectRealization_independence_compiles · IndisputableMonolith/Foundation/PairKernelProductionEffectPhysicalityS26Consumer.lean:116 
def s26_effectRealization_independence_compiles :=
  committedEffects_admit_physicalRealization_split
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

Physical realization is automatic or unconditional. The five-class structure has physical meaning without the realization arrow. The dimension 5 is derived in this declaration; it is imported from elsewhere in the framework.

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.

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:

MACHINE LAYER · GROUNDED CLAIM TABLE · CLICK TO EXPAND