AutoSamplingTheory.SALD.cycle151GeneralMovingTargetDiscreteEmGeneratorPointwiseEventSourceFieldLowerObligation

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 cycle151GeneralMovingTargetDiscreteEmGeneratorPointwiseEventSourceFieldLowerObligation :
    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.cycle151_em_generator_pointwise_event_source_field_lower_2

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 151 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField for appendix.tex:984-995 and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the pointwise EM event-field identity hemGeneratorLaplacianEventFieldEqLaplacian is no longer primitive; it follows from the smaller source-cited equality hemGeneratorLaplacianEventFieldEqSourceField identifying the named frozen EM Laplacian event field with the weak-FP source Laplacian field, plus the already tracked hweakFpSourceFieldEqLaplacian. The packet is a direct leaf theorem and does not add a total-event/source-functional consumer wrapper.

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.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField
2. hemGeneratorLaplacianEventFieldEqSourceField
3. hweakFpSourceFieldEqLaplacian
4. appendix.tex:984-995
5. appendix.tex:1379-1387
6. 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_2 worker packet in the EM conditional-law/state-event set-integral illness area. It targets only the direct hemGeneratorLaplacianEventFieldEqLaplacian leaf requested after the lower_1 handoff. No SLT file was consulted or imported; no Lake/toolchain change, theorem-status promotion, non-EM fallback, broad audit, downstream wrapper churn, fake closure, or sald_version_2.tex use.

def cycle151GeneralMovingTargetDiscreteEmGeneratorPointwiseEventSourceFieldLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle151_em_generator_pointwise_event_source_field_lower_2"
  statement := "Cycle 151 lower_2 compiles SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField for appendix.tex:984-995 and appendix.tex:1379-1387. Classification: narrows-source-cited-boundary. Exact boundary narrowed: the pointwise EM event-field identity hemGeneratorLaplacianEventFieldEqLaplacian is no longer primitive; it follows from the smaller source-cited equality hemGeneratorLaplacianEventFieldEqSourceField identifying the named frozen EM Laplacian event field with the weak-FP source Laplacian field, plus the already tracked hweakFpSourceFieldEqLaplacian. The packet is a direct leaf theorem and does not add a total-event/source-functional consumer wrapper."
  source := saldGeneralMovingTargetDiscreteWeakFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.generalMovingTargetDiscreteEmGeneratorLaplacianEventFieldEqLaplacianOfWeakFpSourceField",
    "hemGeneratorLaplacianEventFieldEqSourceField",
    "hweakFpSourceFieldEqLaplacian",
    "appendix.tex:984-995",
    "appendix.tex:1379-1387",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  note := "Dynamic-leaf lower_2 worker packet in the EM conditional-law/state-event set-integral illness area. It targets only the direct hemGeneratorLaplacianEventFieldEqLaplacian leaf requested after the lower_1 handoff. No SLT file was consulted or imported; no Lake/toolchain change, theorem-status promotion, non-EM fallback, broad audit, downstream wrapper churn, fake closure, or sald_version_2.tex use."

/-- Cycle-151 lower_2 proof-DAG pane for the pointwise event-field source-field
leaf. -/