AutoSamplingTheory.SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianDag

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 cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianDag :
    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.cycle148.middle_packet.em_generator_laplacian_law_integral_from_state_event_current_pointwise
interface : String (explicit)
Text describing intended mathematical interface.
Compiled helper reuse: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula derives hemGeneratorLaplacianLawIntegral by applying the source-cited EM state-event equality to Set.univ.
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.cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula
2. sald.general_moving_target_discrete.em_interpolation_fp
3. 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.cycle148.middle_packet.weak_fp_source_action_em_generator_pointwise_event_state_event_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula feeds the state-event split through the current pointwise event/trace Laplacian route, replacing only hemGeneratorLaplacianLawIntegral while keeping hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian 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.cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventLawIntegralTraceLaplacianFormula
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.formalized — stored label only; no proof certification
id : String (explicit)
Stable plan-node identifier.
ASTIS.SALD.cycle148.remaining_state_event_pointwise_event_and_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 148 middle: prove the source-cited EM conditional-law/state-event formula for the named frozen EM Laplacian contribution, namely hemGeneratorLaplacianTotalEventIntegral and hemGeneratorLaplacianStateEventEqLaplacian, and still prove hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian. The older hemGeneratorLaplacianLawIntegral now follows locally from the state-event formula.
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula
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.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.cycle148.reviewer_pointwise_state_event_trace_laplacian_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianLawIntegral is narrowed to the source-cited EM conditional-law/state-event formula through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula, 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.cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventLawIntegralTraceLaplacianFormula
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. cycle 148 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 cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle148.middle_packet.em_generator_laplacian_law_integral_from_state_event_current_pointwise"
      interface := "Compiled helper reuse: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula derives hemGeneratorLaplacianLawIntegral by applying the source-cited EM state-event equality to Set.univ."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle148.middle_packet.weak_fp_source_action_em_generator_pointwise_event_state_event_trace_laplacian"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula feeds the state-event split through the current pointwise event/trace Laplacian route, replacing only hemGeneratorLaplacianLawIntegral while keeping hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventLawIntegralTraceLaplacianFormula",
        "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.formalized
    },
    {
      id := "ASTIS.SALD.cycle148.remaining_state_event_pointwise_event_and_trace_laplacian"
      interface := "Remaining exact theorem boundary after cycle 148 middle: prove the source-cited EM conditional-law/state-event formula for the named frozen EM Laplacian contribution, namely hemGeneratorLaplacianTotalEventIntegral and hemGeneratorLaplacianStateEventEqLaplacian, and still prove hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian. The older hemGeneratorLaplacianLawIntegral now follows locally from the state-event formula."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianLawIntegralOfStateEventFormula",
        "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.cycle148.reviewer_pointwise_state_event_trace_laplacian_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianLawIntegral is narrowed to the source-cited EM conditional-law/state-event formula through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula, 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.cycle148GeneralMovingTargetDiscreteEmGeneratorPointwiseStateEventTraceLaplacianMiddleObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStateEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventLawIntegralTraceLaplacianFormula",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 148 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 148 lower_1: state-event pointwise scout -/

/-- Cycle-148 lower_1 scout for the state-event equality left by the current
state-event trace-Laplacian route. -/

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