AutoSamplingTheory.SALD.cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceFieldSourceEventDag

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 cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceFieldSourceEventDag :
    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.lower_2_packet.total_event_from_trace_field_source_and_event

   interface : String (explicit)

   Text describing intended mathematical interface.

   Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorTraceActionDef, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldEqLaplacian, and hsourceLaplacianFunctional by reconstructing hemGeneratorStdBasisDef and hemGeneratorLaplacianEventFieldStdBasisDef, then applying the cycle-149 lower_1 total-event 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.cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceFieldSourceEventLowerObligation
   2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula
   3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceAndEventFormula
   4. SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField
   5. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField
   6. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
   7. hemGeneratorTraceActionDef
   8. hemGeneratorLaplacianEventFieldEqTraceField
   9. htraceFieldEqLaplacian
   10. hsourceLaplacianFunctional
   11. appendix.tex:984-995
   12. appendix.tex:1368-1387
   13. 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.lower_2_remaining_trace_action_event_trace_laplacian

   interface : String (explicit)

   Text describing intended mathematical interface.

   Remaining exact theorem boundary after cycle 149 lower_2: prove hemGeneratorTraceActionDef for the named frozen EM Laplacian action, hemGeneratorLaplacianEventFieldEqTraceField identifying the named event field with the trace field, and htraceFieldEqLaplacian. Keep hsourceLaplacianFunctional and state-event equality explicit when they are not supplied by pointwise rewriting.

   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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula
   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 cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceFieldSourceEventDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle149.lower_2_packet.total_event_from_trace_field_source_and_event"
      interface := "Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorTraceActionDef, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldEqLaplacian, and hsourceLaplacianFunctional by reconstructing hemGeneratorStdBasisDef and hemGeneratorLaplacianEventFieldStdBasisDef, then applying the cycle-149 lower_1 total-event theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle149GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceFieldSourceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfStdBasisSourceAndEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
        "hemGeneratorTraceActionDef",
        "hemGeneratorLaplacianEventFieldEqTraceField",
        "htraceFieldEqLaplacian",
        "hsourceLaplacianFunctional",
        "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.lower_2_remaining_trace_action_event_trace_laplacian"
      interface := "Remaining exact theorem boundary after cycle 149 lower_2: prove hemGeneratorTraceActionDef for the named frozen EM Laplacian action, hemGeneratorLaplacianEventFieldEqTraceField identifying the named event field with the trace field, and htraceFieldEqLaplacian. Keep hsourceLaplacianFunctional and state-event equality explicit when they are not supplied by pointwise rewriting."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula",
        "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 150: total-event trace law-integral source leaf -/

/-- Cycle-150 middle narrowing for the trace-action definition left by the
current total-event trace-field route. -/