AutoSamplingTheory.SALD.cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventStdBasisSourceFunctionalDag

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 cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventStdBasisSourceFunctionalDag :
    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.cycle149.packet.total_event_from_stdbasis_source_functional

   interface : String (explicit)

   Text describing intended mathematical interface.

   Compiled source-boundary bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceFunctional derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorStdBasisDef, hsourceLaplacianFunctional, and hemGeneratorLaplacianEventFieldEqLaplacian by first deriving hemGeneratorSourceActionDef through the cycle-141 standard-basis source route, then applying the cycle-148 total-event source-functional theorem.

   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.cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventStdBasisSourceFunctionalLowerObligation
   2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceFunctional
   3. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
   4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional
   5. hemGeneratorStdBasisDef
   6. hsourceLaplacianFunctional
   7. hemGeneratorLaplacianEventFieldEqLaplacian
   8. appendix.tex:984-995
   9. appendix.tex:1368-1387
   10. 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.cycle149.remaining_stdbasis_source_event_trace

   interface : String (explicit)

   Text describing intended mathematical interface.

   Remaining exact theorem boundary after cycle 149: prove the paper's standard-basis source formula hemGeneratorStdBasisDef for the named frozen EM Laplacian action, plus hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian; keep the state-event equality explicit only when it is not supplied by the pointwise rewrite route.

   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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceFunctional
   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 cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventStdBasisSourceFunctionalDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle149.packet.total_event_from_stdbasis_source_functional"
      interface := "Compiled source-boundary bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceFunctional derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorStdBasisDef, hsourceLaplacianFunctional, and hemGeneratorLaplacianEventFieldEqLaplacian by first deriving hemGeneratorSourceActionDef through the cycle-141 standard-basis source route, then applying the cycle-148 total-event source-functional theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventStdBasisSourceFunctionalLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceFunctional",
        "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfSourceFunctional",
        "hemGeneratorStdBasisDef",
        "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.cycle149.remaining_stdbasis_source_event_trace"
      interface := "Remaining exact theorem boundary after cycle 149: prove the paper's standard-basis source formula hemGeneratorStdBasisDef for the named frozen EM Laplacian action, plus hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian; keep the state-event equality explicit only when it is not supplied by the pointwise rewrite route."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceFunctional",
        "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 lower_1 narrowing for the event-field Laplacian identity left
by the standard-basis source-functional total-event route. -/