AutoSamplingTheory.SALD.cycle151GeneralMovingTargetDiscreteEmGeneratorPointwiseEventSourceFieldDag

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 cycle151GeneralMovingTargetDiscreteEmGeneratorPointwiseEventSourceFieldDag :
    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.cycle151.lower_2_packet.pointwise_event_from_source_field

   interface : String (explicit)

   Text describing intended mathematical interface.

   Compiled direct-leaf theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField derives hemGeneratorLaplacianEventFieldEqLaplacian from hemGeneratorLaplacianEventFieldEqSourceField plus hweakFpSourceFieldEqLaplacian.

   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.cycle151GeneralMovingTargetDiscreteEmGeneratorPointwiseEventSourceFieldLowerObligation
   2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField
   3. hemGeneratorLaplacianEventFieldEqSourceField
   4. hweakFpSourceFieldEqLaplacian
   5. appendix.tex:984-995
   6. appendix.tex:1379-1387

   reusedBy : List String (explicit)

   Declared consumers as strings, default empty.

   Ordered data items

   1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
   2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula
   3. sald.general_moving_target_discrete.em_interpolation_fp
   4. 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.cycle151.lower_2_remaining_pointwise_event_source_field

   interface : String (explicit)

   Text describing intended mathematical interface.

   Remaining exact theorem boundary after cycle 151 lower_2: prove hemGeneratorLaplacianEventFieldEqSourceField for the named frozen EM Laplacian event field and keep hweakFpSourceFieldEqLaplacian, htraceFieldEqLaplacian, hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, state-event, and sibling EM leaves explicit.

   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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField
   2. appendix.tex:984-995
   3. 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 cycle151GeneralMovingTargetDiscreteEmGeneratorPointwiseEventSourceFieldDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle151.lower_2_packet.pointwise_event_from_source_field"
      interface := "Compiled direct-leaf theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField derives hemGeneratorLaplacianEventFieldEqLaplacian from hemGeneratorLaplacianEventFieldEqSourceField plus hweakFpSourceFieldEqLaplacian."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle151GeneralMovingTargetDiscreteEmGeneratorPointwiseEventSourceFieldLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField",
        "hemGeneratorLaplacianEventFieldEqSourceField",
        "hweakFpSourceFieldEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle151.lower_2_remaining_pointwise_event_source_field"
      interface := "Remaining exact theorem boundary after cycle 151 lower_2: prove hemGeneratorLaplacianEventFieldEqSourceField for the named frozen EM Laplacian event field and keep hweakFpSourceFieldEqLaplacian, htraceFieldEqLaplacian, hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, state-event, and sibling EM leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-152 direct-leaf narrowing for the EM event-field/source-field
equality. -/