AutoSamplingTheory.SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceDag

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 cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceDag :
    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.cycle141.middle_packet.em_generator_source_action_std_basis
interface : String (explicit)
Text describing intended mathematical interface.
Compiled illness-area theorem: SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula derives hemGeneratorSourceActionDef from hemGeneratorStdBasisDef, the source-cited standard-basis second-derivative formula for the frozen EM generator Laplacian component, using 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.cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
4. Mathlib.Analysis.InnerProductSpace.Laplacian
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula
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.cycle141.middle_packet.weak_fp_source_action_em_generator_std_basis
interface : String (explicit)
Text describing intended mathematical interface.
Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula feeds the standard-basis EM generator source-action split into the cycle-140 source-functional route, replacing the direct hemGeneratorSourceActionDef premise while keeping hlaplacianEqEmGenerator, 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.cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional
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.cycle141.lower_1_packet.em_generator_trace_field_source
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 proof-scout theorem: SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField derives hemGeneratorStdBasisDef from two smaller source-cited facts: hemGeneratorTraceActionDef, identifying the frozen EM generator Laplacian component with the source functional applied to a named trace field, and htraceFieldStdBasis, identifying that trace field pointwise with the standard-basis second derivatives of selectedTest.
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.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceFieldSourceScoutObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField
3. appendix.tex:984-995
4. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula
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.cycle141.lower_1_packet.weak_fp_source_action_em_generator_trace_field
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_1 consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula feeds the trace-field split through the cycle-141 standard-basis EM generator source-action route, replacing the direct hemGeneratorStdBasisDef premise while keeping hlaplacianEqEmGenerator, 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.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceFieldSourceScoutObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula
4. sald.general_moving_target_discrete.em_interpolation_fp
5. 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.cycle141.lower_2_packet.em_generator_trace_law_integral
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula removes hemGeneratorTraceActionDef from the downstream trace-field consumer by deriving it from hemGeneratorTraceLawIntegral, the law-space trace integral against hatRhoS, and the existing hsourceLaplacianFunctional definition. The remaining analytic EM trace facts are hemGeneratorTraceLawIntegral and htraceFieldStdBasis.
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.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceLawIntegralLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula
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.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.cycle141.remaining_em_generator_trace_field_source
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 141 lower_2: prove hlaplacianEqEmGenerator for the selected weak-FP Laplacian action, hemGeneratorTraceLawIntegral for the frozen EM generator Laplacian trace action as a law-space integral against hatRhoS, and htraceFieldStdBasis for the named trace field's pointwise standard-basis second-derivative formula. The direct hemGeneratorTraceActionDef leaf now follows from SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula, hemGeneratorStdBasisDef follows from SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField, and hemGeneratorSourceActionDef follows from SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula. The sibling hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence, and diffusion leaves remain separate.
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
5. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula
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.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.cycle141.reviewer_em_generator_std_basis_source_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorSourceActionDef is narrowed to hemGeneratorStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula, hemGeneratorStdBasisDef is further narrowed to hemGeneratorTraceActionDef plus htraceFieldStdBasis through SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField, and hemGeneratorTraceActionDef is narrowed to hemGeneratorTraceLawIntegral plus hsourceLaplacianFunctional through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula. 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.cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation
2. SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceFieldSourceScoutObligation
3. SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceLawIntegralLowerObligation
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula
5. SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField
6. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula
7. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
8. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula
9. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional
10. appendix.tex:984-995
11. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 141 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 cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle141.middle_packet.em_generator_source_action_std_basis"
      interface := "Compiled illness-area theorem: SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula derives hemGeneratorSourceActionDef from hemGeneratorStdBasisDef, the source-cited standard-basis second-derivative formula for the frozen EM generator Laplacian component, using SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "Mathlib.Analysis.InnerProductSpace.Laplacian",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle141.middle_packet.weak_fp_source_action_em_generator_std_basis"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula feeds the standard-basis EM generator source-action split into the cycle-140 source-functional route, replacing the direct hemGeneratorSourceActionDef premise while keeping hlaplacianEqEmGenerator, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, and hsourceLaplacianFunctional explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional",
        "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.cycle141.lower_1_packet.em_generator_trace_field_source"
      interface := "Compiled lower_1 proof-scout theorem: SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField derives hemGeneratorStdBasisDef from two smaller source-cited facts: hemGeneratorTraceActionDef, identifying the frozen EM generator Laplacian component with the source functional applied to a named trace field, and htraceFieldStdBasis, identifying that trace field pointwise with the standard-basis second derivatives of selectedTest."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceFieldSourceScoutObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle141.lower_1_packet.weak_fp_source_action_em_generator_trace_field"
      interface := "Compiled lower_1 consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula feeds the trace-field split through the cycle-141 standard-basis EM generator source-action route, replacing the direct hemGeneratorStdBasisDef premise while keeping hlaplacianEqEmGenerator, hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, and hsourceLaplacianFunctional explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceFieldSourceScoutObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpLaplacianDefOfSourceLaplacianField",
        "SALD.generalMovingTargetDiscreteTestLaplacianPointwiseOfWeakFpSourceLaplacianField",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle141.lower_2_packet.em_generator_trace_law_integral"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula removes hemGeneratorTraceActionDef from the downstream trace-field consumer by deriving it from hemGeneratorTraceLawIntegral, the law-space trace integral against hatRhoS, and the existing hsourceLaplacianFunctional definition. The remaining analytic EM trace facts are hemGeneratorTraceLawIntegral and htraceFieldStdBasis."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceLawIntegralLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula",
        "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.cycle141.remaining_em_generator_trace_field_source"
      interface := "Remaining exact theorem boundary after cycle 141 lower_2: prove hlaplacianEqEmGenerator for the selected weak-FP Laplacian action, hemGeneratorTraceLawIntegral for the frozen EM generator Laplacian trace action as a law-space integral against hatRhoS, and htraceFieldStdBasis for the named trace field's pointwise standard-basis second-derivative formula. The direct hemGeneratorTraceActionDef leaf now follows from SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula, hemGeneratorStdBasisDef follows from SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField, and hemGeneratorSourceActionDef follows from SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula. The sibling hweakFpSourceFieldEqLaplacian, hsourceLaplacianFieldMeas, hsourceLaplacianFunctional, htestLaplacianStdBasisDef, density-Laplacian source facts, Green/trace/box-divergence, and diffusion leaves remain separate."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula",
        "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.cycle141.reviewer_em_generator_std_basis_source_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorSourceActionDef is narrowed to hemGeneratorStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula, hemGeneratorStdBasisDef is further narrowed to hemGeneratorTraceActionDef plus htraceFieldStdBasis through SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField, and hemGeneratorTraceActionDef is narrowed to hemGeneratorTraceLawIntegral plus hsourceLaplacianFunctional through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula. 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.cycle141GeneralMovingTargetDiscreteEmGeneratorStdBasisSourceLowerObligation",
        "SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceFieldSourceScoutObligation",
        "SALD.cycle141GeneralMovingTargetDiscreteEmGeneratorTraceLawIntegralLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLawIntegralSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorStdBasisDefOfTraceField",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceFieldSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorSourceFunctional",
        "appendix.tex:984-995",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 141 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-142 proof-DAG pane for the EM generator trace state-integral split. -/

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