AutoSamplingTheory.SALD.cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventDag

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventDag :
    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

id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle151.packet.total_event_from_pointwise_event_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula derives the total-event formula from hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqLaplacian, and htraceFieldEqLaplacian. It first recovers hemGeneratorLaplacianEventFieldEqTraceField through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields, then applies the cycle-150 trace-Laplacian state 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.cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula
5. hemGeneratorLaplacianEventFieldEqLaplacian
6. htraceFieldEqLaplacian
7. hemGeneratorLaplacianStateIntegral
8. hsourceLaplacianFieldMeas
9. hsourceLaplacianFunctional
10. appendix.tex:984-995
11. appendix.tex:1368-1387
12. 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.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle151.remaining_trace_laplacian_state_pointwise_event
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 151: prove hemGeneratorLaplacianStateIntegral for the named frozen EM Laplacian selected-test action as a sample-space integral along hatXAtS, prove hsourceLaplacianFieldMeas when not supplied by the source-Laplacian route, prove hemGeneratorLaplacianEventFieldEqLaplacian, and prove 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle151.reviewer_pointwise_event_trace_laplacian_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldEqTraceField is narrowed to hemGeneratorLaplacianEventFieldEqLaplacian plus htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula, remaining direct leaves stay explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, wrapper churn, or sald_version_2 use.
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.cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
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. cycle 151 reviewer
status : AutoSamplingTheory.ProofStatus (explicit)
Recorded workflow status, default planned.
AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle151.packet.total_event_from_pointwise_event_trace_laplacian"
      interface := "Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula derives the total-event formula from hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqLaplacian, and htraceFieldEqLaplacian. It first recovers hemGeneratorLaplacianEventFieldEqTraceField through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields, then applies the cycle-150 trace-Laplacian state total-event theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula",
        "hemGeneratorLaplacianEventFieldEqLaplacian",
        "htraceFieldEqLaplacian",
        "hemGeneratorLaplacianStateIntegral",
        "hsourceLaplacianFieldMeas",
        "hsourceLaplacianFunctional",
        "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.formalized
    },
    {
      id := "ASTIS.SALD.cycle151.remaining_trace_laplacian_state_pointwise_event"
      interface := "Remaining exact theorem boundary after cycle 151: prove hemGeneratorLaplacianStateIntegral for the named frozen EM Laplacian selected-test action as a sample-space integral along hatXAtS, prove hsourceLaplacianFieldMeas when not supplied by the source-Laplacian route, prove hemGeneratorLaplacianEventFieldEqLaplacian, and prove htraceFieldEqLaplacian. Keep hsourceLaplacianFunctional and state-event equality explicit when they are not supplied by pointwise rewriting."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula",
        "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
    },
    {
      id := "ASTIS.SALD.cycle151.reviewer_pointwise_event_trace_laplacian_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldEqTraceField is narrowed to hemGeneratorLaplacianEventFieldEqLaplacian plus htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula, remaining direct leaves stay explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, wrapper churn, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle151GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralPointwiseEventObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 151 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-151 lower_2 direct-leaf narrowing for the pointwise EM event-field
Laplacian identity. -/

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