AutoSamplingTheory.SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorTotalEventSourceFunctionalDag

Data definition / provenance and workflow record

Meaning and type

The result has data type List AutoSamplingTheory.ProofDagBlock. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle148GeneralMovingTargetDiscreteEmGeneratorTotalEventSourceFunctionalDag :
    List ProofDagBlock

Construction and field-by-field explanation

Construct an ordered list of the following data items. It is not a logical conjunction or proof DAG.

This Lean definition constructs provenance or workflow data. It does not prove the mathematical statements stored as text. Status labels, named dependencies and citations are data, not compilation, proof or source certificates.

Ordered data items

1. id : String (explicit)

   Stable plan-node identifier.

   ASTIS.SALD.cycle148.lower_2_packet.total_event_from_source_functional

   interface : String (explicit)

   Text describing intended mathematical interface.

   Compiled source leaf: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorSourceActionDef, hsourceLaplacianFunctional, and hemGeneratorLaplacianEventFieldEqLaplacian by rewriting the law integral over Set.univ.

   source : AutoSamplingTheory.SourceAnchor (explicit)

   Source pointer.

   AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge

   targetLean : String (explicit)

   Textual planned implementation destination.

   AutoSamplingTheory/SALD.lean

   dependsOn : List String (explicit)

   Declared input names as strings, default empty.

   Ordered data items

   1. SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorTotalEventSourceFunctionalLowerObligation
   2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional
   3. hemGeneratorSourceActionDef
   4. hsourceLaplacianFunctional
   5. hemGeneratorLaplacianEventFieldEqLaplacian
   6. appendix.tex:984-995
   7. appendix.tex:1368-1387
   8. appendix.tex:1379-1387

   reusedBy : List String (explicit)

   Declared consumers as strings, default empty.

   Ordered data items

   1. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula
   2. sald.general_moving_target_discrete.em_interpolation_fp
   3. sald.discrete_forward_kl.em_interpolation_fp

   status : AutoSamplingTheory.ProofStatus (explicit)

   Recorded workflow status, default planned.

   AutoSamplingTheory.ProofStatus.formalized — stored label only; no proof certification

2. id : String (explicit)

   Stable plan-node identifier.

   ASTIS.SALD.cycle148.lower_2_remaining_source_functional_state_event_trace

   interface : String (explicit)

   Text describing intended mathematical interface.

   Remaining exact theorem boundary after cycle 148 lower_2: prove the source-functional action definition for the named frozen EM Laplacian action, prove hemGeneratorLaplacianStateEventEqLaplacian when it is not supplied through the pointwise route, and still prove hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian. The total-event formula now follows locally from the source-functional action definition plus the event-field identity.

   source : AutoSamplingTheory.SourceAnchor (explicit)

   Source pointer.

   AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge

   targetLean : String (explicit)

   Textual planned implementation destination.

   AutoSamplingTheory/SALD.lean

   dependsOn : List String (explicit)

   Declared input names as strings, default empty.

   Ordered data items

   1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional
   2. appendix.tex:984-995
   3. appendix.tex:1368-1387
   4. appendix.tex:1379-1387

   reusedBy : List String (explicit)

   Declared consumers as strings, default empty.

   Ordered data items

   1. sald.general_moving_target_discrete.em_interpolation_fp
   2. sald.discrete_forward_kl.em_interpolation_fp

   status : AutoSamplingTheory.ProofStatus (explicit)

   Recorded workflow status, default planned.

   AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

def cycle148GeneralMovingTargetDiscreteEmGeneratorTotalEventSourceFunctionalDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle148.lower_2_packet.total_event_from_source_functional"
      interface := "Compiled source leaf: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorSourceActionDef, hsourceLaplacianFunctional, and hemGeneratorLaplacianEventFieldEqLaplacian by rewriting the law integral over Set.univ."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorTotalEventSourceFunctionalLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional",
        "hemGeneratorSourceActionDef",
        "hsourceLaplacianFunctional",
        "hemGeneratorLaplacianEventFieldEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle148.lower_2_remaining_source_functional_state_event_trace"
      interface := "Remaining exact theorem boundary after cycle 148 lower_2: prove the source-functional action definition for the named frozen EM Laplacian action, prove hemGeneratorLaplacianStateEventEqLaplacian when it is not supplied through the pointwise route, and still prove hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian. The total-event formula now follows locally from the source-functional action definition plus the event-field identity."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 149: total-event standard-basis source-functional leaf -/

/-- Cycle-149 narrowing for the source-functional action definition left by
the cycle-148 total-event route. -/