AutoSamplingTheory.SALD.cycle155GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralLaplacianFieldDag

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 cycle155GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralLaplacianFieldDag :
    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.cycle155.packet.trace_state_integral_from_laplacian_state_integral
interface : String (explicit)
Text describing intended mathematical interface.
Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField derives hemGeneratorTraceStateIntegral from hemGeneratorLaplacianStateIntegral and htraceFieldEqLaplacian by rewriting the sample-space trace-field integrand along hatXAtS.
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.cycle155GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralLaplacianFieldLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField
3. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfTraceStateIntegralLaplacianField
4. hemGeneratorLaplacianStateIntegral
5. htraceFieldEqLaplacian
6. appendix.tex:984-995
7. appendix.tex:1368-1387
8. appendix.tex:1379-1387
reusedBy : List String (explicit)
Declared consumers as strings, default empty.
Ordered data items
1. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfTraceStateIntegralLaplacianField
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.cycle155.remaining_trace_state_integral_laplacian_field
interface : String (explicit)
Text describing intended mathematical interface.
Remaining exact theorem boundary after cycle 155: prove hemGeneratorLaplacianStateIntegral or one of its smaller accepted source-functional leaves, prove htraceFieldMeas for the map-law transport, and prove htraceFieldEqLaplacian for the named trace field. Keep hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, state-event, and sibling EM 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.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField
2. SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfTraceStateIntegralLaplacianField
3. hemGeneratorLaplacianStateIntegral
4. htraceFieldMeas
5. htraceFieldEqLaplacian
6. appendix.tex:984-995
7. appendix.tex:1368-1387
8. 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.cycle155.reviewer_trace_state_laplacian_field_check
interface : String (explicit)
Text describing intended mathematical interface.
Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorTraceStateIntegral is narrowed to hemGeneratorLaplacianStateIntegral plus htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField, htraceFieldMeas remains explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, downstream 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.cycle155GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralLaplacianFieldLowerObligation
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField
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. cycle 155 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 cycle155GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralLaplacianFieldDag :
    List ProofDagBlock :=
  [
    {
      id := "ASTIS.SALD.cycle155.packet.trace_state_integral_from_laplacian_state_integral"
      interface := "Compiled theorem: SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField derives hemGeneratorTraceStateIntegral from hemGeneratorLaplacianStateIntegral and htraceFieldEqLaplacian by rewriting the sample-space trace-field integrand along hatXAtS."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle155GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralLaplacianFieldLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfTraceStateIntegralLaplacianField",
        "hemGeneratorLaplacianStateIntegral",
        "htraceFieldEqLaplacian",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := [
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfTraceStateIntegralLaplacianField",
        "sald.general_moving_target_discrete.em_interpolation_fp",
        "sald.discrete_forward_kl.em_interpolation_fp"
      ]
      status := ProofStatus.formalized
    },
    {
      id := "ASTIS.SALD.cycle155.remaining_trace_state_integral_laplacian_field"
      interface := "Remaining exact theorem boundary after cycle 155: prove hemGeneratorLaplacianStateIntegral or one of its smaller accepted source-functional leaves, prove htraceFieldMeas for the map-law transport, and prove htraceFieldEqLaplacian for the named trace field. Keep hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, state-event, and sibling EM leaves explicit."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField",
        "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianStateIntegralOfTraceStateIntegralLaplacianField",
        "hemGeneratorLaplacianStateIntegral",
        "htraceFieldMeas",
        "htraceFieldEqLaplacian",
        "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.cycle155.reviewer_trace_state_laplacian_field_check"
      interface := "Reviewer check: accept only if the packet classification is narrows-source-cited-boundary, hemGeneratorTraceStateIntegral is narrowed to hemGeneratorLaplacianStateIntegral plus htraceFieldEqLaplacian through SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField, htraceFieldMeas remains explicit, and python3 tools/astis.py check passes without SLT import, non-EM fallback, theorem-status promotion, fake closure, broad audit, Lake/toolchain change, downstream wrapper churn, or sald_version_2 use."
      source := saldGeneralMovingTargetDiscreteWeakFpSource
      targetLean := "AutoSamplingTheory/SALD.lean"
      dependsOn := [
        "SALD.cycle155GeneralMovingTargetDiscreteEmGeneratorTraceStateIntegralLaplacianFieldLowerObligation",
        "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField",
        "appendix.tex:984-995",
        "appendix.tex:1368-1387",
        "appendix.tex:1379-1387"
      ]
      reusedBy := ["cycle 155 reviewer"]
      status := ProofStatus.obligation
    }
  ]

/-! ### Cycle 156: trace-field equality from pointwise trace identity -/

/-- Cycle-156 narrowing of the trace-field/Laplacian source boundary. -/

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