AutoSamplingTheory.SALD.cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.ProofObligation. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation :
    ProofObligation

Construction and field-by-field explanation

Construct a data record from explicit fields and the audited defaults shown below.

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.

id : String (explicit)

Stable obligation identifier.

sald.general_moving_target_discrete.cycle156_em_generator_trace_field_pointwise

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 156 compiles SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise, SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis, and SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundaries narrowed: htraceFieldEqLaplacian for the named frozen EM trace field follows from the smaller pointwise source identity htraceFieldPointwiseEqLaplacian by function extensionality; htraceFieldPointwiseEqLaplacian follows from the smaller pointwise standard-basis Hessian-trace display htraceFieldPointwiseStdBasis plus SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv; htraceFieldPointwiseStdBasis follows from the smaller source-facing pair hemGeneratorLaplacianEventFieldEqTraceField plus hemGeneratorLaplacianEventFieldStdBasisDef. The packet keeps hemGeneratorLaplacianStateIntegral, htraceFieldMeas, hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hemGeneratorLaplacianEventFieldEqTraceField, hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, state-event, and sibling EM leaves explicit.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteWeakFpSource — audited data reference, not expanded and not a compiled dependency edge

status : AutoSamplingTheory.ProofStatus (explicit)

Stored ProofStatus, default obligation; even an explicitly stored formalized does not independently certify a Lean theorem.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

dependsOn : List String (explicit)

List of declared dependency names as strings; may mix theorem names, obligations, source labels, or descriptions. Not the compiled dependency DAG.

Ordered data items

1. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise
2. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis
3. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. htraceFieldEqLaplacian
6. htraceFieldPointwiseEqLaplacian
7. htraceFieldPointwiseStdBasis
8. hemGeneratorLaplacianEventFieldEqTraceField
9. hemGeneratorLaplacianEventFieldStdBasisDef
10. SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField
11. SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField
12. appendix.tex:984-995
13. appendix.tex:1368-1387
14. appendix.tex:1379-1387
15. sald.general_moving_target_discrete.em_interpolation_fp

note : String (explicit)

Recorded evidence/caveats; may distinguish a compiled scalar helper from still-open source analysis.

Illness-area refiner packet for the EM conditional-law/state-event backend. It implements only the requested htraceFieldEqLaplacian-to-pointwise narrowing and does not add a stale hemGeneratorTraceLawIntegral/hemGeneratorTraceStateIntegral wrapper, downstream total-event/source-functional consumer, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, non-EM fallback, or sald_version_2.tex content.

def cycle156GeneralMovingTargetDiscreteEmGeneratorTraceFieldPointwiseLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle156_em_generator_trace_field_pointwise"
  statement := "Cycle 156 compiles SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise, SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis, and SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundaries narrowed: htraceFieldEqLaplacian for the named frozen EM trace field follows from the smaller pointwise source identity htraceFieldPointwiseEqLaplacian by function extensionality; htraceFieldPointwiseEqLaplacian follows from the smaller pointwise standard-basis Hessian-trace display htraceFieldPointwiseStdBasis plus SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv; htraceFieldPointwiseStdBasis follows from the smaller source-facing pair hemGeneratorLaplacianEventFieldEqTraceField plus hemGeneratorLaplacianEventFieldStdBasisDef. The packet keeps hemGeneratorLaplacianStateIntegral, htraceFieldMeas, hsourceLaplacianFunctional, hsourceLaplacianFieldMeas, hemGeneratorLaplacianEventFieldEqTraceField, hemGeneratorLaplacianEventFieldStdBasisDef, hweakFpSourceFieldPointwiseEqLaplacian, state-event, and sibling EM leaves explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldEqLaplacianOfPointwise",
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseEqLaplacianOfStdBasis",
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldPointwiseStdBasisOfEventFieldStdBasis",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "htraceFieldEqLaplacian",
    "htraceFieldPointwiseEqLaplacian",
    "htraceFieldPointwiseStdBasis",
    "hemGeneratorLaplacianEventFieldEqTraceField",
    "hemGeneratorLaplacianEventFieldStdBasisDef",
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceStateIntegralOfLaplacianStateIntegralLaplacianField",
    "SALD.generalMovingTargetDiscreteEmGeneratorTraceFieldStdBasisOfLaplacianField",
    "appendix.tex:984-995",
    "appendix.tex:1368-1387",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Illness-area refiner packet for the EM conditional-law/state-event backend. It implements only the requested htraceFieldEqLaplacian-to-pointwise narrowing and does not add a stale hemGeneratorTraceLawIntegral/hemGeneratorTraceStateIntegral wrapper, downstream total-event/source-functional consumer, SLT import, Lake/toolchain change, theorem-status promotion, fake closure, broad audit, non-EM fallback, or sald_version_2.tex content."

/-- Cycle-156 proof-DAG pane for the trace-field pointwise split. -/