AutoSamplingTheory.SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventDag

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 cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventDag :
    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.cycle145.lower_2_packet.em_generator_laplacian_event_field_std_basis_from_trace_field
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField derives hemGeneratorLaplacianEventFieldStdBasisDef from hemGeneratorLaplacianEventFieldEqTraceField and htraceFieldStdBasis by transitivity of function equality.
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.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField
3. appendix.tex:984-995
4. appendix.tex:1368-1387
5. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
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.cycle145.lower_2_packet.weak_fp_source_action_em_generator_trace_event_law_integral
interface : String (explicit)
Text describing intended mathematical interface.
Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula feeds the trace-field event split through the cycle-145 law-integral route, replacing only hemGeneratorLaplacianEventFieldStdBasisDef while keeping hemGeneratorLaplacianLawIntegral 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.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
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
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle145.lower_2_remaining_em_generator_law_integral_and_trace_event_equality
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 145 lower_2: prove hemGeneratorLaplacianLawIntegral and the source equality hemGeneratorLaplacianEventFieldEqTraceField identifying the named frozen EM Laplacian event field with the already tracked trace field. The old event-field standard-basis definition now follows locally from that equality 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField
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.cycle145.lower_2_reviewer_trace_event_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldStdBasisDef is narrowed to hemGeneratorLaplacianEventFieldEqTraceField plus htraceFieldStdBasis through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula, hemGeneratorLaplacianLawIntegral 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.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField
4. SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation
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 cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle145.lower_2_packet.em_generator_laplacian_event_field_std_basis_from_trace_field"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField derives hemGeneratorLaplacianEventFieldStdBasisDef from hemGeneratorLaplacianEventFieldEqTraceField and htraceFieldStdBasis by transitivity of function equality."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle145.lower_2_packet.weak_fp_source_action_em_generator_trace_event_law_integral"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula feeds the trace-field event split through the cycle-145 law-integral route, replacing only hemGeneratorLaplacianEventFieldStdBasisDef while keeping hemGeneratorLaplacianLawIntegral and sibling source leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
        "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.lower_2_remaining_em_generator_law_integral_and_trace_event_equality"
      interface := "Remaining exact theorem boundary after cycle 145 lower_2: prove hemGeneratorLaplacianLawIntegral and the source equality hemGeneratorLaplacianEventFieldEqTraceField identifying the named frozen EM Laplacian event field with the already tracked trace field. The old event-field standard-basis definition now follows locally from that equality and htraceFieldStdBasis."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStdBasisEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField",
        "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.lower_2_reviewer_trace_event_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldStdBasisDef is narrowed to hemGeneratorLaplacianEventFieldEqTraceField plus htraceFieldStdBasis through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula, hemGeneratorLaplacianLawIntegral 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.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianTraceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventLawIntegralFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldStdBasisDefOfTraceField",
        "SALD.cycle145GeneralMovingTargetDiscreteEmGeneratorLaplacianStdBasisLawLowerObligation",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 145 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 146: EM generator trace-event total-event boundary -/

/-- Cycle-146 narrowing for the law-space generator Laplacian integral under
the latest trace-event route. -/

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