AutoSamplingTheory.SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralDag

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 cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralDag :
    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.cycle142.middle_packet.em_generator_trace_law_integral_state_transport
interface : String (explicit)
Text describing intended mathematical interface.
Compiled middle theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral derives hemGeneratorTraceLawIntegral from hemGeneratorTraceStateIntegral, hatRhoS = Measure.map hatXAtS P, AEMeasurable hatXAtS, and trace-field measurability under hatRhoS, using MeasureTheory.integral_map.
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.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralMiddleObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral
3. MeasureTheory.integral_map
4. appendix.tex:984-995
5. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula
3. sald.general_moving_target_discrete.em_interpolation_fp
4. 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.cycle142.middle_packet.weak_fp_source_action_em_generator_trace_state_integral
interface : String (explicit)
Text describing intended mathematical interface.
Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula feeds the state-integral trace split through the cycle-141 trace-law route, replacing the direct hemGeneratorTraceLawIntegral premise while keeping hlaplacianEqEmGenerator, htraceFieldStdBasis, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, and hsourceLaplacianFunctional explicit.
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.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula
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.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField
2. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField
3. sald.general_moving_target_discrete.em_interpolation_fp
4. 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.cycle142.lower_1_packet.trace_field_meas_from_source_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas derives htraceFieldMeas from hsourceLaplacianFieldMeas and htraceFieldStdBasis by identifying the named trace field with Mathlib's Laplacian through SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv.
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.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianStateIntegralScoutObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
4. Mathlib.Analysis.InnerProductSpace.Laplacian
5. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula
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.cycle142.lower_1_packet.em_generator_trace_state_from_laplacian_state
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral derives hemGeneratorTraceStateIntegral from hemGeneratorLaplacianStateIntegral and htraceFieldStdBasis by replacing the trace-field integrand with Mathlib's selected-test Laplacian.
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.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianStateIntegralScoutObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
4. appendix.tex:984-995
5. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula
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.cycle142.lower_1_packet.weak_fp_source_action_em_generator_trace_laplacian_state
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula feeds the Laplacian state-integral split through the cycle-142 trace-state route, replacing direct htraceFieldMeas and hemGeneratorTraceStateIntegral while keeping hlaplacianEqEmGenerator, htraceFieldStdBasis, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, and hsourceLaplacianFunctional explicit.
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.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianStateIntegralScoutObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas
5. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral
6. appendix.tex:984-995
7. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField
2. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField
3. sald.general_moving_target_discrete.em_interpolation_fp
4. 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.cycle142.lower_2_packet.em_generator_laplacian_law_integral
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula derives the trace-Laplacian state-integral consumer from the law-space selected-test Laplacian generator identity hemGeneratorLaplacianLawIntegral, using SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral and MeasureTheory.integral_map to recover hemGeneratorLaplacianStateIntegral.
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.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianLawIntegralLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula
5. MeasureTheory.integral_map
6. appendix.tex:984-995
7. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField
2. SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField
3. sald.general_moving_target_discrete.em_interpolation_fp
4. 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.cycle142.remaining_em_generator_trace_state_integral
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 142 lower_2: prove hlaplacianEqEmGenerator for the selected weak-FP Laplacian action, hemGeneratorLaplacianLawIntegral for the frozen EM generator selected-test Laplacian action as a law-space integral against hatRhoS, and htraceFieldStdBasis for the named trace field's pointwise standard-basis second-derivative formula. The sample-space hemGeneratorLaplacianStateIntegral now follows from the law integral by SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral; htraceFieldMeas follows from hsourceLaplacianFieldMeas; and hemGeneratorTraceStateIntegral follows from the selected-test Laplacian state integral via SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv.
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula
2. SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianLawIntegralLowerObligation
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas
5. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral
6. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
7. SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral
8. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula
9. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula
10. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
11. appendix.tex:984-995
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.obligation — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle142.reviewer_em_generator_trace_state_integral_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianStateIntegral is narrowed to hemGeneratorLaplacianLawIntegral through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula, hemGeneratorTraceStateIntegral and htraceFieldMeas remain narrowed through the lower_1 trace-Laplacian route, sibling EM/weak-FP source leaves remain explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, wrapper churn, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, 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.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianLawIntegralLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
4. SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianStateIntegralScoutObligation
5. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula
6. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas
7. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral
8. SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralMiddleObligation
9. SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral
10. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula
11. appendix.tex:984-995
12. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 142 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 cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle142.middle_packet.em_generator_trace_law_integral_state_transport"
      interface := "Compiled middle theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral derives hemGeneratorTraceLawIntegral from hemGeneratorTraceStateIntegral, hatRhoS = Measure.map hatXAtS P, AEMeasurable hatXAtS, and trace-field measurability under hatRhoS, using MeasureTheory.integral_map."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral",
        "MeasureTheory.integral_map",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle142.middle_packet.weak_fp_source_action_em_generator_trace_state_integral"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula feeds the state-integral trace split through the cycle-141 trace-law route, replacing the direct hemGeneratorTraceLawIntegral premise while keeping hlaplacianEqEmGenerator, htraceFieldStdBasis, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, and hsourceLaplacianFunctional explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralMiddleObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle142.lower_1_packet.trace_field_meas_from_source_laplacian"
      interface := "Compiled lower_1 theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas derives htraceFieldMeas from hsourceLaplacianFieldMeas and htraceFieldStdBasis by identifying the named trace field with Mathlib's Laplacian through SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianStateIntegralScoutObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "Mathlib.Analysis.InnerProductSpace.Laplacian",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle142.lower_1_packet.em_generator_trace_state_from_laplacian_state"
      interface := "Compiled lower_1 theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral derives hemGeneratorTraceStateIntegral from hemGeneratorLaplacianStateIntegral and htraceFieldStdBasis by replacing the trace-field integrand with Mathlib's selected-test Laplacian."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianStateIntegralScoutObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle142.lower_1_packet.weak_fp_source_action_em_generator_trace_laplacian_state"
      interface := "Compiled lower_1 consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula feeds the Laplacian state-integral split through the cycle-142 trace-state route, replacing direct htraceFieldMeas and hemGeneratorTraceStateIntegral while keeping hlaplacianEqEmGenerator, htraceFieldStdBasis, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, and hsourceLaplacianFunctional explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianStateIntegralScoutObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle142.lower_2_packet.em_generator_laplacian_law_integral"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula derives the trace-Laplacian state-integral consumer from the law-space selected-test Laplacian generator identity hemGeneratorLaplacianLawIntegral, using SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral and MeasureTheory.integral_map to recover hemGeneratorLaplacianStateIntegral."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianLawIntegralLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula",
        "MeasureTheory.integral_map",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle142.remaining_em_generator_trace_state_integral"
      interface := "Remaining exact theorem boundary after cycle 142 lower_2: prove hlaplacianEqEmGenerator for the selected weak-FP Laplacian action, hemGeneratorLaplacianLawIntegral for the frozen EM generator selected-test Laplacian action as a law-space integral against hatRhoS, and htraceFieldStdBasis for the named trace field's pointwise standard-basis second-derivative formula. The sample-space hemGeneratorLaplacianStateIntegral now follows from the law integral by SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral; htraceFieldMeas follows from hsourceLaplacianFieldMeas; and hemGeneratorTraceStateIntegral follows from the selected-test Laplacian state integral via SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula",
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianLawIntegralLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "appendix.tex:984-995",
        "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.cycle142.reviewer_em_generator_trace_state_integral_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianStateIntegral is narrowed to hemGeneratorLaplacianLawIntegral through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula, hemGeneratorTraceStateIntegral and htraceFieldMeas remain narrowed through the lower_1 trace-Laplacian route, sibling EM/weak-FP source leaves remain explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, wrapper churn, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianLawIntegralLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianLawIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceLaplacianStateIntegralScoutObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldMeasOfSourceLaplacianFieldMeas",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegral",
        "SALD.cycle142GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceLawIntegralOfStateIntegral",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceStateIntegralSourceFormula",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 142 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 143: EM generator Laplacian law integral via state events -/

/-- Cycle-143 state-event narrowing for the frozen EM generator Laplacian law
integral. -/

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