AutoSamplingTheory.SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventDag

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 cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventDag :
    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.cycle146.middle_packet.em_generator_trace_event_total_event
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula feeds the total-state-event formula through the current trace-event law-integral route. It derives hemGeneratorLaplacianLawIntegral from hemGeneratorLaplacianTotalEventIntegral, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldStdBasis, and the local Mathlib standard-basis Laplacian bridge.
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.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
5. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
6. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
7. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField
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.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.cycle146.remaining_em_generator_total_event_and_trace_event
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 146: prove hemGeneratorLaplacianTotalEventIntegral for the named frozen EM Laplacian event field, prove hemGeneratorLaplacianEventFieldEqTraceField identifying that event field with the trace field, and prove htraceFieldStdBasis. The older hemGeneratorLaplacianLawIntegral now follows locally from the total-state-event formula plus the trace-event standard-basis 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
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.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.cycle146.reviewer_trace_event_total_event_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianLawIntegral is narrowed to hemGeneratorLaplacianTotalEventIntegral plus hemGeneratorLaplacianEventFieldEqTraceField and htraceFieldStdBasis through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula, sibling EM/weak-FP source leaves remain 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.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula
3. SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation
4. SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianStateEventLowerObligation
5. appendix.tex:984-995
6. appendix.tex:1368-1387
7. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 146 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 cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle146.middle_packet.em_generator_trace_event_total_event"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula feeds the total-state-event formula through the current trace-event law-integral route. It derives hemGeneratorLaplacianLawIntegral from hemGeneratorLaplacianTotalEventIntegral, hemGeneratorLaplacianEventFieldEqTraceField, htraceFieldStdBasis, and the local Mathlib standard-basis Laplacian bridge."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField",
        "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.cycle146.remaining_em_generator_total_event_and_trace_event"
      interface := "Remaining exact theorem boundary after cycle 146: prove hemGeneratorLaplacianTotalEventIntegral for the named frozen EM Laplacian event field, prove hemGeneratorLaplacianEventFieldEqTraceField identifying that event field with the trace field, and prove htraceFieldStdBasis. The older hemGeneratorLaplacianLawIntegral now follows locally from the total-state-event formula plus the trace-event standard-basis route."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
        "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.cycle146.reviewer_trace_event_total_event_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianLawIntegral is narrowed to hemGeneratorLaplacianTotalEventIntegral plus hemGeneratorLaplacianEventFieldEqTraceField and htraceFieldStdBasis through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula, sibling EM/weak-FP source leaves remain 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.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceEventTotalEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventFormula",
        "SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation",
        "SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianStateEventLowerObligation",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 146 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 146 lower_1: EM trace-field Laplacian boundary -/

/-- Cycle-146 lower_1 narrowing for the trace-field standard-basis formula
inside the latest trace-event total-event route. -/

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