AutoSamplingTheory.SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventDag

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 cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventDag :
    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.cycle146.lower_2_packet.em_generator_laplacian_event_field_trace_from_laplacian_fields
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields derives hemGeneratorLaplacianEventFieldEqTraceField from hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian by transitivity through Mathlib's selected-test Laplacian.
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.cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula
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.cycle146.lower_2_packet.weak_fp_source_action_em_generator_pointwise_event_total_event_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula feeds the pointwise event-field Laplacian split through the lower_1 trace-field Laplacian route, replacing only hemGeneratorLaplacianEventFieldEqTraceField while keeping hemGeneratorLaplacianTotalEventIntegral 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.cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula
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.cycle146.lower_2_remaining_total_event_pointwise_event_and_trace_laplacian
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 146 lower_2: prove hemGeneratorLaplacianTotalEventIntegral, prove hemGeneratorLaplacianEventFieldEqLaplacian, and prove htraceFieldEqLaplacian. The older hemGeneratorLaplacianEventFieldEqTraceField now follows locally from the two Laplacian identities.
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
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.cycle146.lower_2_reviewer_pointwise_trace_event_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldEqTraceField is narrowed to hemGeneratorLaplacianEventFieldEqLaplacian plus htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula, 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.cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields
4. SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianLowerObligation
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 146 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 cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle146.lower_2_packet.em_generator_laplacian_event_field_trace_from_laplacian_fields"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields derives hemGeneratorLaplacianEventFieldEqTraceField from hemGeneratorLaplacianEventFieldEqLaplacian and htraceFieldEqLaplacian by transitivity through Mathlib's selected-test Laplacian."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle146.lower_2_packet.weak_fp_source_action_em_generator_pointwise_event_total_event_trace_laplacian"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula feeds the pointwise event-field Laplacian split through the lower_1 trace-field Laplacian route, replacing only hemGeneratorLaplacianEventFieldEqTraceField while keeping hemGeneratorLaplacianTotalEventIntegral and htraceFieldEqLaplacian explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianTraceEventTotalEventTraceLaplacianFormula",
        "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.cycle146.lower_2_remaining_total_event_pointwise_event_and_trace_laplacian"
      interface := "Remaining exact theorem boundary after cycle 146 lower_2: prove hemGeneratorLaplacianTotalEventIntegral, prove hemGeneratorLaplacianEventFieldEqLaplacian, and prove htraceFieldEqLaplacian. The older hemGeneratorLaplacianEventFieldEqTraceField now follows locally from the two Laplacian identities."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "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.cycle146.lower_2_reviewer_pointwise_trace_event_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianEventFieldEqTraceField is narrowed to hemGeneratorLaplacianEventFieldEqLaplacian plus htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula, 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.cycle146GeneralMovingTargetDiscreteEmGeneratorPointwiseTraceEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventTotalEventTraceLaplacianFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqTraceFieldOfLaplacianFields",
        "SALD.cycle146GeneralMovingTargetDiscreteEmGeneratorTraceFieldLaplacianLowerObligation",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 146 lower_2 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 147: EM pointwise action-definition trace-Laplacian boundary -/

/-- Cycle-147 narrowing for the total-event formula inside the current
pointwise trace-event route. -/

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