AutoSamplingTheory.SALD.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventDag

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 cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventDag :
    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.cycle150.middle_packet.trace_action_from_trace_law_integral
interface : String (explicit)
Text describing intended mathematical interface.
Compiled helper: SALD.generalMovingTargetDiscreteEmGeneratorTraceActionDefOfTraceLawIntegral derives hemGeneratorTraceActionDef from the law-space source fact hemGeneratorTraceLawIntegral and the already explicit source-functional definition hsourceLaplacianFunctional.
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.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventMiddleObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceActionDefOfTraceLawIntegral
3. hemGeneratorTraceLawIntegral
4. hsourceLaplacianFunctional
5. appendix.tex:984-995
6. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle150.middle_packet.total_event_from_trace_law_integral_source_and_event
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorTraceLawIntegral, hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqTraceField, and htraceFieldEqLaplacian by first recovering hemGeneratorTraceActionDef, then applying the cycle-149 trace-field source/event 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.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventMiddleObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceActionDefOfTraceLawIntegral
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula
5. hemGeneratorTraceLawIntegral
6. hsourceLaplacianFunctional
7. hemGeneratorLaplacianEventFieldEqTraceField
8. htraceFieldEqLaplacian
9. appendix.tex:984-995
10. appendix.tex:1368-1387
11. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle150.lower_1_packet.total_event_from_trace_state_integral_source_and_event
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorTraceStateIntegral, hhatRhoS, hhatX, htraceFieldMeas, hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqTraceField, and htraceFieldEqLaplacian by first recovering hemGeneratorTraceLawIntegral through SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral, then applying the cycle-150 trace-law 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.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceStateIntegralSourceEventLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula
5. hemGeneratorTraceStateIntegral
6. hhatRhoS
7. hhatX
8. htraceFieldMeas
9. hsourceLaplacianFunctional
10. hemGeneratorLaplacianEventFieldEqTraceField
11. htraceFieldEqLaplacian
12. appendix.tex:984-995
13. appendix.tex:1368-1387
14. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle150.lower_2_packet.total_event_from_trace_laplacian_state_integral_source_and_event
interface : String (explicit)
Text describing intended mathematical interface.
Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hhatRhoS, hhatX, hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqTraceField, and htraceFieldEqLaplacian by first recovering htraceFieldMeas and hemGeneratorTraceStateIntegral through the local trace-field/Laplacian helpers, then applying the cycle-150 trace-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.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralSourceEventLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
4. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas
5. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral
6. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula
7. hemGeneratorLaplacianStateIntegral
8. hsourceLaplacianFieldMeas
9. hhatRhoS
10. hhatX
11. hsourceLaplacianFunctional
12. hemGeneratorLaplacianEventFieldEqTraceField
13. htraceFieldEqLaplacian
14. appendix.tex:984-995
15. appendix.tex:1368-1387
16. 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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle150.lower_2_remaining_trace_laplacian_state_event_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 150 lower_2: 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 hemGeneratorLaplacianEventFieldEqTraceField, 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula
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.cycle150.lower_1_remaining_trace_state_event_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 150 lower_1: prove hemGeneratorTraceStateIntegral for the named frozen EM Laplacian trace action as a sample-space integral along hatXAtS, prove htraceFieldMeas when not supplied by the trace-field/source-Laplacian route, prove hemGeneratorLaplacianEventFieldEqTraceField, 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula
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.cycle150.remaining_trace_law_event_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 150 middle: prove hemGeneratorTraceLawIntegral for the named frozen EM Laplacian trace action as a law-space integral against hatRhoS, prove hemGeneratorLaplacianEventFieldEqTraceField, 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula
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.cycle150.reviewer_trace_law_total_event_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorTraceActionDef is narrowed to hemGeneratorTraceLawIntegral plus hsourceLaplacianFunctional through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula, 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.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventMiddleObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceActionDefOfTraceLawIntegral
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula
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 150 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 cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle150.middle_packet.trace_action_from_trace_law_integral"
      interface := "Compiled helper: SALD.generalMovingTargetDiscreteEmGeneratorTraceActionDefOfTraceLawIntegral derives hemGeneratorTraceActionDef from the law-space source fact hemGeneratorTraceLawIntegral and the already explicit source-functional definition hsourceLaplacianFunctional."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceActionDefOfTraceLawIntegral",
        "hemGeneratorTraceLawIntegral",
        "hsourceLaplacianFunctional",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle150.middle_packet.total_event_from_trace_law_integral_source_and_event"
      interface := "Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorTraceLawIntegral, hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqTraceField, and htraceFieldEqLaplacian by first recovering hemGeneratorTraceActionDef, then applying the cycle-149 trace-field source/event total-event theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceActionDefOfTraceLawIntegral",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula",
        "hemGeneratorTraceLawIntegral",
        "hsourceLaplacianFunctional",
        "hemGeneratorLaplacianEventFieldEqTraceField",
        "htraceFieldEqLaplacian",
        "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.cycle150.lower_1_packet.total_event_from_trace_state_integral_source_and_event"
      interface := "Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorTraceStateIntegral, hhatRhoS, hhatX, htraceFieldMeas, hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqTraceField, and htraceFieldEqLaplacian by first recovering hemGeneratorTraceLawIntegral through SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral, then applying the cycle-150 trace-law total-event theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceStateIntegralSourceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula",
        "hemGeneratorTraceStateIntegral",
        "hhatRhoS",
        "hhatX",
        "htraceFieldMeas",
        "hsourceLaplacianFunctional",
        "hemGeneratorLaplacianEventFieldEqTraceField",
        "htraceFieldEqLaplacian",
        "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.cycle150.lower_2_packet.total_event_from_trace_laplacian_state_integral_source_and_event"
      interface := "Compiled bridge: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula derives hemGeneratorLaplacianTotalEventIntegral from hemGeneratorLaplacianStateIntegral, hsourceLaplacianFieldMeas, hhatRhoS, hhatX, hsourceLaplacianFunctional, hemGeneratorLaplacianEventFieldEqTraceField, and htraceFieldEqLaplacian by first recovering htraceFieldMeas and hemGeneratorTraceStateIntegral through the local trace-field/Laplacian helpers, then applying the cycle-150 trace-state total-event theorem."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLaplacianStateIntegralSourceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula",
        "hemGeneratorLaplacianStateIntegral",
        "hsourceLaplacianFieldMeas",
        "hhatRhoS",
        "hhatX",
        "hsourceLaplacianFunctional",
        "hemGeneratorLaplacianEventFieldEqTraceField",
        "htraceFieldEqLaplacian",
        "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.cycle150.lower_2_remaining_trace_laplacian_state_event_trace_laplacian"
      interface := "Remaining exact theorem boundary after cycle 150 lower_2: 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 hemGeneratorLaplacianEventFieldEqTraceField, 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula",
        "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.cycle150.lower_1_remaining_trace_state_event_trace_laplacian"
      interface := "Remaining exact theorem boundary after cycle 150 lower_1: prove hemGeneratorTraceStateIntegral for the named frozen EM Laplacian trace action as a sample-space integral along hatXAtS, prove htraceFieldMeas when not supplied by the trace-field/source-Laplacian route, prove hemGeneratorLaplacianEventFieldEqTraceField, 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceStateIntegralSourceAndEventFormula",
        "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.cycle150.remaining_trace_law_event_trace_laplacian"
      interface := "Remaining exact theorem boundary after cycle 150 middle: prove hemGeneratorTraceLawIntegral for the named frozen EM Laplacian trace action as a law-space integral against hatRhoS, prove hemGeneratorLaplacianEventFieldEqTraceField, 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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula",
        "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.cycle150.reviewer_trace_law_total_event_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorTraceActionDef is narrowed to hemGeneratorTraceLawIntegral plus hsourceLaplacianFunctional through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula, 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.cycle150GeneralMovingTargetDiscreteEmGeneratorTotalEventTraceLawIntegralSourceEventMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceActionDefOfTraceLawIntegral",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLawIntegralSourceAndEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceFieldSourceAndEventFormula",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 150 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-151 direct-leaf narrowing for the event-field/trace-field equality
left by the current trace-Laplacian state total-event route. -/

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