AutoSamplingTheory.SALD.cycle147GeneralMovingTargetDiscreteEmGeneratorPointwiseStdBasisActionTraceLaplacianLowerObligation

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 cycle147GeneralMovingTargetDiscreteEmGeneratorPointwiseStdBasisActionTraceLaplacianLowerObligation :
    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.cycle147_em_generator_pointwise_stdbasis_action_trace_laplacian

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 147 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionPointwiseEventFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStdBasisActionTraceLaplacianFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianActionDef premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefTraceLaplacianFormula is no longer primitive; it follows from the source standard-basis action integral hemGeneratorLaplacianStdBasisActionDef together with the already explicit pointwise event-field Laplacian identity hemGeneratorLaplacianEventFieldEqLaplacian and SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv. hemGeneratorLaplacianStdBasisActionDef, hemGeneratorLaplacianEventFieldEqLaplacian, htraceFieldEqLaplacian, hlaplacianEqEmGenerator, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion leaves remain 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.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionPointwiseEventFormula
2. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStdBasisActionTraceLaplacianFormula
3. SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefTraceLaplacianFormula
4. SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv
5. Mathlib.Analysis.InnerProductSpace.Laplacian
6. appendix.tex:984-995
7. appendix.tex:1368-1387
8. appendix.tex:1379-1387
9. 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.

Dynamic-leaf lower_1 proof-scout packet inside the cycle-142/143/144/145/146/147 EM generator trace-state illness area. It rejects wrapper churn by replacing only hemGeneratorLaplacianActionDef with the source standard-basis action formula, using the existing event-field/Laplacian premise and local Mathlib Laplacian standard-basis bridge. It does not prove hemGeneratorLaplacianStdBasisActionDef, prove hemGeneratorLaplacianEventFieldEqLaplacian, prove htraceFieldEqLaplacian, prove hlaplacianEqEmGenerator, close source-field/source-functional leaves, promote density-Laplacian/Green/trace/box-divergence/diffusion leaves, import SLT, change Lake/toolchain files, use sald_version_2, close a theorem by fake proof, or take a non-EM fallback.

def cycle147GeneralMovingTargetDiscreteEmGeneratorPointwiseStdBasisActionTraceLaplacianLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle147_em_generator_pointwise_stdbasis_action_trace_laplacian"
  statement := "Cycle 147 lower_1 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionPointwiseEventFormula and SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStdBasisActionTraceLaplacianFormula for appendix.tex:984-995, appendix.tex:1368-1387, and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the hemGeneratorLaplacianActionDef premise left by SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefTraceLaplacianFormula is no longer primitive; it follows from the source standard-basis action integral hemGeneratorLaplacianStdBasisActionDef together with the already explicit pointwise event-field Laplacian identity hemGeneratorLaplacianEventFieldEqLaplacian and SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv. hemGeneratorLaplacianStdBasisActionDef, hemGeneratorLaplacianEventFieldEqLaplacian, htraceFieldEqLaplacian, hlaplacianEqEmGenerator, source-field/source-functional leaves, density-Laplacian, Green/trace/box-divergence, and diffusion leaves remain explicit."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianActionDefOfStdBasisActionPointwiseEventFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventStdBasisActionTraceLaplacianFormula",
    "SALD.generalMovingTargetDiscreteWeakFpSourceActionDefOfEmGeneratorTraceLaplacianPointwiseEventActionDefTraceLaplacianFormula",
    "SALD.generalMovingTargetDiscreteSourceTestLaplacianEqStdIteratedFDeriv",
    "Mathlib.Analysis.InnerProductSpace.Laplacian",
    "appendix.tex:984-995",
    "appendix.tex:1368-1387",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower_1 proof-scout packet inside the cycle-142/143/144/145/146/147 EM generator trace-state illness area. It rejects wrapper churn by replacing only hemGeneratorLaplacianActionDef with the source standard-basis action formula, using the existing event-field/Laplacian premise and local Mathlib Laplacian standard-basis bridge. It does not prove hemGeneratorLaplacianStdBasisActionDef, prove hemGeneratorLaplacianEventFieldEqLaplacian, prove htraceFieldEqLaplacian, prove hlaplacianEqEmGenerator, close source-field/source-functional leaves, promote density-Laplacian/Green/trace/box-divergence/diffusion leaves, import SLT, change Lake/toolchain files, use sald_version_2, close a theorem by fake proof, or take a non-EM fallback."

/-- Cycle-147 lower-1 proof-DAG pane for the standard-basis action narrowing
inside the pointwise event/trace-Laplacian route. -/