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

AutoSamplingTheory.SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDag

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 cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDag :
    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.cycle144.lower_2_packet.em_generator_laplacian_action_std_basis_action
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula derives hemGeneratorLaplacianActionDef from the source-facing standard-basis action integral hemGeneratorLaplacianStdBasisActionDef and the event-field standard-basis definition hemGeneratorLaplacianEventFieldStdBasisDef by rewriting the integrand under the Set.univ state integral.
    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.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionLowerObligation
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula
    3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
    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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
    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.cycle144.lower_2_packet.weak_fp_source_action_em_generator_trace_laplacian_std_basis_action
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula feeds the standard-basis action split through the cycle-144 standard-basis event consumer, replacing only hemGeneratorLaplacianActionDef 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.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionLowerObligation
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula
    3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula
    4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
    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.cycle144.lower_2_remaining_em_generator_laplacian_std_basis_action_and_event_defs
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact theorem boundary after cycle 144 lower_2: prove the source standard-basis action integral hemGeneratorLaplacianStdBasisActionDef and the source standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian event field. The older action definition and pointwise Mathlib-Laplacian equality now follow 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula
    3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
    4. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
    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.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.cycle144.lower_2_reviewer_em_generator_laplacian_std_basis_action_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianActionDef is narrowed to hemGeneratorLaplacianStdBasisActionDef plus hemGeneratorLaplacianEventFieldStdBasisDef through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula, 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.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionLowerObligation
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula
    3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula
    4. SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation
    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 144 lower_2 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 cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle144.lower_2_packet.em_generator_laplacian_action_std_basis_action"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula derives hemGeneratorLaplacianActionDef from the source-facing standard-basis action integral hemGeneratorLaplacianStdBasisActionDef and the event-field standard-basis definition hemGeneratorLaplacianEventFieldStdBasisDef by rewriting the integrand under the Set.univ state integral."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle144.lower_2_packet.weak_fp_source_action_em_generator_trace_laplacian_std_basis_action"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula feeds the standard-basis action split through the cycle-144 standard-basis event consumer, replacing only hemGeneratorLaplacianActionDef while keeping hemGeneratorLaplacianEventFieldStdBasisDef and sibling source leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
        "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.cycle144.lower_2_remaining_em_generator_laplacian_std_basis_action_and_event_defs"
      interface := "Remaining exact theorem boundary after cycle 144 lower_2: prove the source standard-basis action integral hemGeneratorLaplacianStdBasisActionDef and the source standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian event field. The older action definition and pointwise Mathlib-Laplacian equality now follow locally."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
        "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.cycle144.lower_2_reviewer_em_generator_laplacian_std_basis_action_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianActionDef is narrowed to hemGeneratorLaplacianStdBasisActionDef plus hemGeneratorLaplacianEventFieldStdBasisDef through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula, 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.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisActionLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventStdBasisActionFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionFormula",
        "SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 144 lower_2 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 145: EM generator law-integral to standard-basis action boundary -/

/-- Cycle-145 law-integral narrowing for the frozen EM generator
standard-basis Laplacian action definition. -/

Existing module entry · Audited data-reader index · All teaching coverage