AutoSamplingTheory.SALD.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalDag

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 cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalDag :
    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.cycle153.packet.laplacian_state_integral_from_source_functional
interface : String (explicit)
Text describing intended mathematical interface.
Compiled direct-leaf theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional derives hemGeneratorLaplacianStateIntegral from hemGeneratorSourceActionDef plus hsourceLaplacianFunctional, then reuses SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral to transport the law-space Laplacian integral along hatXAtS.
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.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
4. hemGeneratorSourceActionDef
5. hsourceLaplacianFunctional
6. hsourceLaplacianFieldMeas
7. appendix.tex:984-995
8. appendix.tex:1368-1387
9. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula
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.cycle153.lower_2_packet.laplacian_state_integral_from_stdbasis_source_functional
interface : String (explicit)
Text describing intended mathematical interface.
Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional derives hemGeneratorLaplacianStateIntegral from hemGeneratorStdBasisDef by first recovering hemGeneratorSourceActionDef through SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula, then reusing SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional.
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.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralStdBasisSourceFunctionalLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional
3. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional
5. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
6. hemGeneratorStdBasisDef
7. hsourceLaplacianFunctional
8. hsourceLaplacianFieldMeas
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.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula
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.cycle153.lower_2_remaining_laplacian_state_integral_stdbasis_source_functional
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 153 lower_2: prove hemGeneratorStdBasisDef for the named frozen EM Laplacian action as the sourceLaplacianFunctional applied to the standard-basis second derivatives of selectedTest. The broader hemGeneratorSourceActionDef now follows locally; keep hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, htraceFieldEqLaplacian, state-event, and sibling EM leaves 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.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional
2. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
3. hemGeneratorStdBasisDef
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.cycle153.reviewer_laplacian_state_integral_source_functional_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 first to hemGeneratorSourceActionDef plus hsourceLaplacianFunctional through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional and then, for lower_2, hemGeneratorSourceActionDef is narrowed to hemGeneratorStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional. Sibling EM/weak-FP 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.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalLowerObligation
2. SALD.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralStdBasisSourceFunctionalLowerObligation
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional
4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional
5. SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula
6. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral
7. appendix.tex:984-995
8. appendix.tex:1368-1387
9. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. cycle 153 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 cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle153.packet.laplacian_state_integral_from_source_functional"
      interface := "Compiled direct-leaf theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional derives hemGeneratorLaplacianStateIntegral from hemGeneratorSourceActionDef plus hsourceLaplacianFunctional, then reuses SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral to transport the law-space Laplacian integral along hatXAtS."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
        "hemGeneratorSourceActionDef",
        "hsourceLaplacianFunctional",
        "hsourceLaplacianFieldMeas",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle153.lower_2_packet.laplacian_state_integral_from_stdbasis_source_functional"
      interface := "Compiled lower_2 theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional derives hemGeneratorLaplacianStateIntegral from hemGeneratorStdBasisDef by first recovering hemGeneratorSourceActionDef through SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula, then reusing SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralStdBasisSourceFunctionalLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional",
        "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
        "hemGeneratorStdBasisDef",
        "hsourceLaplacianFunctional",
        "hsourceLaplacianFieldMeas",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianTotalEventIntegralOfTraceLaplacianStateIntegralSourceAndPointwiseEventFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle153.lower_2_remaining_laplacian_state_integral_stdbasis_source_functional"
      interface := "Remaining exact theorem boundary after cycle 153 lower_2: prove hemGeneratorStdBasisDef for the named frozen EM Laplacian action as the sourceLaplacianFunctional applied to the standard-basis second derivatives of selectedTest. The broader hemGeneratorSourceActionDef now follows locally; keep hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, htraceFieldEqLaplacian, state-event, and sibling EM leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional",
        "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
        "hemGeneratorStdBasisDef",
        "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.cycle153.reviewer_laplacian_state_integral_source_functional_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianStateIntegral is narrowed first to hemGeneratorSourceActionDef plus hsourceLaplacianFunctional through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional and then, for lower_2, hemGeneratorSourceActionDef is narrowed to hemGeneratorStdBasisDef through SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional. Sibling EM/weak-FP 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.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralSourceFunctionalLowerObligation",
        "SALD.cycle153GeneralMovingTargetDiscreteEmGeneratorLaplacianStateIntegralStdBasisSourceFunctionalLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfSourceFunctional",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfStdBasisSourceFunctional",
        "SALD.generalMovingTargetDiscreteEmGeneratorSourceActionDefOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfLawIntegral",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 153 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 154: EM generator Laplacian state integral from trace field -/

/-- Cycle-154 narrowing of the state-integral standard-basis source premise. -/

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