Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawDag

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 cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawDag :
    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

  1. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle145.middle_packet.em_generator_laplacian_std_basis_action_from_law_integral
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula derives hemGeneratorLaplacianStdBasisActionDef from hemGeneratorLaplacianLawIntegral by rewriting the law-space Mathlib Laplacian integral to the Set.univ standard-basis source action.
    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.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula
    3. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
    4. Mathlib.Analysis.InnerProductSpace.Laplacian
    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. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula
    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
  2. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle145.middle_packet.weak_fp_source_action_em_generator_trace_laplacian_law_integral
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula feeds the law-integral split through the cycle-144 standard-basis action consumer, replacing only hemGeneratorLaplacianStdBasisActionDef while keeping hemGeneratorLaplacianEventFieldStdBasisDef and sibling source 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.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
    3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula
    4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula
    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. 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
  3. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle145.remaining_em_generator_law_integral_and_std_basis_event_defs
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact theorem boundary after cycle 145: prove the source law-space EM generator Laplacian action integral hemGeneratorLaplacianLawIntegral and the source standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian event field. The old standard-basis action integral now follows locally.
    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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula
    3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula
    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
  4. id : String (explicit)

    Stable plan-node identifier.

    ASTIS.SALD.cycle145.reviewer_em_generator_laplacian_law_integral_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianStdBasisActionDef is narrowed to hemGeneratorLaplacianLawIntegral plus the local Mathlib standard-basis Laplacian rewrite, hemGeneratorLaplacianEventFieldStdBasisDef remains explicit, 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.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
    3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula
    4. SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionLowerObligation
    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 145 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 cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle145.middle_packet.em_generator_laplacian_std_basis_action_from_law_integral"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula derives hemGeneratorLaplacianStdBasisActionDef from hemGeneratorLaplacianLawIntegral by rewriting the law-space Mathlib Laplacian integral to the Set.univ standard-basis source action."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "Mathlib.Analysis.InnerProductSpace.Laplacian",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle145.middle_packet.weak_fp_source_action_em_generator_trace_laplacian_law_integral"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula feeds the law-integral split through the cycle-144 standard-basis action consumer, replacing only hemGeneratorLaplacianStdBasisActionDef while keeping hemGeneratorLaplacianEventFieldStdBasisDef and sibling source leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "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.cycle145.remaining_em_generator_law_integral_and_std_basis_event_defs"
      interface := "Remaining exact theorem boundary after cycle 145: prove the source law-space EM generator Laplacian action integral hemGeneratorLaplacianLawIntegral and the source standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian event field. The old standard-basis action integral now follows locally."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula",
        "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.cycle145.reviewer_em_generator_laplacian_law_integral_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianStdBasisActionDef is narrowed to hemGeneratorLaplacianLawIntegral plus the local Mathlib standard-basis Laplacian rewrite, hemGeneratorLaplacianEventFieldStdBasisDef remains explicit, 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.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDefOfLawIntegralFormula",
        "SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionLowerObligation",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 145 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 145 lower_2: EM generator trace-field event boundary -/

/-- Cycle-145 lower_2 narrowing for the frozen EM generator Laplacian
event-field standard-basis definition. -/

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