AutoSamplingTheory.SALD.cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation :
    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.cycle69_em_fp_source_signs_lower

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 69 lower compiles SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff for appendix.tex lines 1379-1387: once the analytic weak conditional Fokker-Planck backend supplies partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + sigmaCoeff*Delta hat rho_s and the source coefficient identity sigmaCoeff=sigma_eta^2/2, the wrapper preserves the exact source signs and coefficient for the EM interpolation FP interface.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — 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

SALD.cycle69MainSkeletonAnalyticMiddleObligation
SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff
SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
SALD.generalMovingTargetDiscreteConditionalDriftContract
SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
sald.general_moving_target_discrete.em_interpolation_fp
FokkerPlanckContract
KLContract
FIContract

note : String (explicit)

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

Proof-producing coefficient/sign wrapper only. Common probability space, endpoint laws, regular conditional drift, density/absolute-continuity, weak Fokker-Planck, KL differentiation, integration by parts, LSI, DV, Gronwall, and theorem status remain obligations.

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 cycle69GeneralMovingTargetDiscreteEmFpSourceSignsLowerObligation :
    ProofObligation where
  id := "sald.general_moving_target_discrete.cycle69_em_fp_source_signs_lower"
  statement := "Cycle 69 lower compiles SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff for appendix.tex lines 1379-1387: once the analytic weak conditional Fokker-Planck backend supplies partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + sigmaCoeff*Delta hat rho_s and the source coefficient identity sigmaCoeff=sigma_eta^2/2, the wrapper preserves the exact source signs and coefficient for the EM interpolation FP interface."
  source := saldGeneralMovingTargetDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle69MainSkeletonAnalyticMiddleObligation",
    "SALD.generalMovingTargetDiscreteConditionalFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "FokkerPlanckContract",
    "KLContract",
    "FIContract"
  ]
  note := "Proof-producing coefficient/sign wrapper only. Common probability space, endpoint laws, regular conditional drift, density/absolute-continuity, weak Fokker-Planck, KL differentiation, integration by parts, LSI, DV, Gronwall, and theorem status remain obligations."

/-- Cycle-70 middle obligation for the conditional-law/measurability slice. -/

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