AutoSamplingTheory.SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventDag

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 cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventDag :
    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.cycle143.lower_1_packet.em_generator_laplacian_state_event_pointwise
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise derives the measurable-state-event equality from the pointwise identification emGeneratorLaplacianEventField phi = fun x => Laplacian.laplacian (selectedTest phi) x.
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.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula
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.cycle143.lower_1_packet.weak_fp_source_action_em_generator_trace_laplacian_pointwise_event
interface : String (explicit)
Text describing intended mathematical interface.
Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula feeds the pointwise event-field split through the cycle-143 state-event route, replacing only hemGeneratorLaplacianStateEventEqLaplacian while keeping 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.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula
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.cycle143.lower_1_remaining_em_generator_laplacian_pointwise_event_formula
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 143 lower_1: prove the source-cited EM total-event action for the named frozen-generator Laplacian event field and prove the pointwise event-field identity with Laplacian.laplacian (selectedTest phi). The all-measurable-state-event equality 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.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
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.cycle143.lower_1_reviewer_em_generator_laplacian_pointwise_event_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianStateEventEqLaplacian is narrowed to hemGeneratorLaplacianEventFieldEqLaplacian through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula, 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.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise
4. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula
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 143 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 cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle143.lower_1_packet.em_generator_laplacian_state_event_pointwise"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise derives the measurable-state-event equality from the pointwise identification emGeneratorLaplacianEventField phi = fun x => Laplacian.laplacian (selectedTest phi) x."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle143.lower_1_packet.weak_fp_source_action_em_generator_trace_laplacian_pointwise_event"
      interface := "Compiled consumer theorem: SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula feeds the pointwise event-field split through the cycle-143 state-event route, replacing only hemGeneratorLaplacianStateEventEqLaplacian while keeping sibling source leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula",
        "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.cycle143.lower_1_remaining_em_generator_laplacian_pointwise_event_formula"
      interface := "Remaining exact theorem boundary after cycle 143 lower_1: prove the source-cited EM total-event action for the named frozen-generator Laplacian event field and prove the pointwise event-field identity with Laplacian.laplacian (selectedTest phi). The all-measurable-state-event equality now follows locally."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
        "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.cycle143.lower_1_reviewer_em_generator_laplacian_pointwise_event_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorLaplacianStateEventEqLaplacian is narrowed to hemGeneratorLaplacianEventFieldEqLaplacian through SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula, 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.cycle143GeneralMovingTargetDiscreteEmGeneratorLaplacianPointwiseEventLowerObligation",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventFormula",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateEventEqOfPointwise",
        "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianStateEventFormula",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 143 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-- Cycle-143 lower-2 action-definition narrowing for the frozen EM generator
Laplacian total-event formula. -/

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