AutoSamplingTheory.SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorStateEventPointwiseScoutDag

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 cycle148GeneralMovingTargetDiscreteEmGeneratorStateEventPointwiseScoutDag :
    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_1_packet.state_event_eq_from_pointwise

   interface : String (explicit)

   Text describing intended mathematical interface.

   Proof route: derive hemGeneratorLaplacianStateEventEqLaplacian from hemGeneratorLaplacianEventFieldEqLaplacian by applying SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise. For htests, phi, and measurable state event t, rewrite emGeneratorLaplacianEventField phi to fun x => Laplacian.laplacian (selectedTest phi) x inside the set integral.

   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.cycle148GeneralMovingTargetDiscreteEmGeneratorStateEventPointwiseScoutObligation
   2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
   3. hemGeneratorLaplacianEventFieldEqLaplacian
   4. appendix.tex:984-995
   5. appendix.tex:1368-1387
   6. appendix.tex:1379-1387

   reusedBy : List String (explicit)

   Declared consumers as strings, default empty.

   Ordered data items

   1. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula
   2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula

   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_1_reject_duplicate_state_event_wrapper

   interface : String (explicit)

   Text describing intended mathematical interface.

   Do not add a new theorem whose signature is just the cycle-148 state-event consumer with hemGeneratorLaplacianStateEventEqLaplacian replaced by hemGeneratorLaplacianEventFieldEqLaplacian; that duplicates the already compiled pointwise total-event trace-Laplacian consumer. The useful next implementation block is one genuine source leaf, not another consumer wrapper.

   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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula
   2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula
   3. appendix.tex:984-995
   4. appendix.tex:1368-1387
   5. appendix.tex:1379-1387

   reusedBy : List String (explicit)

   Declared consumers as strings, default empty.

   Ordered data items

   1. cycle 148 lower_2 handoff

   status : AutoSamplingTheory.ProofStatus (explicit)

   Recorded workflow status, default planned.

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

def cycle148GeneralMovingTargetDiscreteEmGeneratorStateEventPointwiseScoutDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle148.lower_1_packet.state_event_eq_from_pointwise"
      interface := "Proof route: derive hemGeneratorLaplacianStateEventEqLaplacian from hemGeneratorLaplacianEventFieldEqLaplacian by applying SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise. For htests, phi, and measurable state event t, rewrite emGeneratorLaplacianEventField phi to fun x => Laplacian.laplacian (selectedTest phi) x inside the set integral."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorStateEventPointwiseScoutObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
        "hemGeneratorLaplacianEventFieldEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle148.lower_1_reject_duplicate_state_event_wrapper"
      interface := "Do not add a new theorem whose signature is just the cycle-148 state-event consumer with hemGeneratorLaplacianStateEventEqLaplacian replaced by hemGeneratorLaplacianEventFieldEqLaplacian; that duplicates the already compiled pointwise total-event trace-Laplacian consumer. The useful next implementation block is one genuine source leaf, not another consumer wrapper."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 148 lower_2 handoff"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 148 lower_2: total-event source-functional leaf -/

/-- Cycle-148 lower_2 narrowing for the total-event action formula left by
the state-event trace-Laplacian route. -/