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

AutoSamplingTheory.SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventDag

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 cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventDag :
    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.middle_packet.em_generator_laplacian_event_field_std_basis
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula derives hemGeneratorLaplacianEventFieldEqLaplacian from the source-facing standard-basis definition hemGeneratorLaplacianEventFieldStdBasisDef by reusing 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.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
    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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula
    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.middle_packet.weak_fp_source_action_em_generator_trace_laplacian_std_basis_event
    interface : String (explicit)

    Text describing intended mathematical interface.

    Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula feeds the standard-basis event-field split through the cycle-143 action-definition route, replacing only hemGeneratorLaplacianEventFieldEqLaplacian while keeping hemGeneratorLaplacianActionDef 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.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
    3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
    4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula
    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.remaining_em_generator_laplacian_std_basis_event_and_action_def
    interface : String (explicit)

    Text describing intended mathematical interface.

    Remaining exact theorem boundary after cycle 144: prove the source action definition hemGeneratorLaplacianActionDef and the source standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian event field. The older pointwise equality with Mathlib Laplacian 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
    2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
    3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula
    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.cycle144.reviewer_em_generator_laplacian_std_basis_event_check
    interface : String (explicit)

    Text describing intended mathematical interface.

    Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldEqLaplacian is narrowed to hemGeneratorLaplacianEventFieldStdBasisDef through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula, hemGeneratorLaplacianActionDef 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, 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.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation
    2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula
    3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula
    4. SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianActionDefLowerObligation
    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 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 cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle144.middle_packet.em_generator_laplacian_event_field_std_basis"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula derives hemGeneratorLaplacianEventFieldEqLaplacian from the source-facing standard-basis definition hemGeneratorLaplacianEventFieldStdBasisDef by reusing SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
        "Mathlib.Analysis.InnerProductSpace.Laplacian",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle144.middle_packet.weak_fp_source_action_em_generator_trace_laplacian_std_basis_event"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula feeds the standard-basis event-field split through the cycle-143 action-definition route, replacing only hemGeneratorLaplacianEventFieldEqLaplacian while keeping hemGeneratorLaplacianActionDef and sibling source leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula",
        "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.remaining_em_generator_laplacian_std_basis_event_and_action_def"
      interface := "Remaining exact theorem boundary after cycle 144: prove the source action definition hemGeneratorLaplacianActionDef and the source standard-basis event-field definition hemGeneratorLaplacianEventFieldStdBasisDef for the named frozen EM Laplacian event field. The older pointwise equality with Mathlib Laplacian now follows locally."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefFormula",
        "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.reviewer_em_generator_laplacian_std_basis_event_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldEqLaplacian is narrowed to hemGeneratorLaplacianEventFieldStdBasisDef through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula, hemGeneratorLaplacianActionDef 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, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle144GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventActionDefFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqOfStdBasisSourceFormula",
        "SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianActionDefLowerObligation",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 144 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 144 lower_2: EM generator standard-basis action boundary -/

/-- Cycle-144 lower-2 standard-basis action narrowing for the frozen EM
generator Laplacian action definition. -/

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