AutoSamplingTheory.SALD.cycle35DiscreteForwardKlEmFpMiddleObligation

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 cycle35DiscreteForwardKlEmFpMiddleObligation : 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.discrete_forward_kl.cycle35_em_fp_middle

statement : String (explicit)

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

Maintain the cycle 35 middle source-to-Lean map for appendix.tex lines 260-385: use the compiled endpoint-vector lemmas and divergence-regrouping lemma as local algebra, while keeping stochastic endpoint laws, conditional drift density/measurability, the conditional-drift Fokker-Planck equation, Laplacian split, boundary integration by parts, and stitched regularity as explicit obligations.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteConditionalFpSource — 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.cycle35DiscreteForwardKlEmFpMiddleContract
2. SALD.cycle35DiscreteForwardKlEmFpUpperPacket
3. SALD.discreteForwardKlEmInterpolationLeftEndpointVector
4. SALD.discreteForwardKlEmInterpolationRightEndpointVector
5. SALD.discreteForwardKlConditionalFpDivergenceDriftSplit
6. SALD.discreteForwardKlEmInterpolationSideConditionContract
7. SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract
8. SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract
9. sald.discrete_forward_kl.em_endpoint_laws
10. sald.discrete_forward_kl.conditional_drift_density
11. sald.discrete_forward_kl.em_conditional_fokker_planck
12. sald.discrete_forward_kl.em_interpolation_fp
13. sald.discrete_forward_kl.stitched_interval_regularity
14. FokkerPlanckContract
15. KLContract
16. FIContract

note : String (explicit)

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

This middle obligation records proof-producing local algebra for the EM interpolation endpoint and conditional-FP regrouping only. It does not mark endpoint law matching, the conditional Fokker-Planck theorem, density/boundary regularity, KL derivative, LSI, DV, Gronwall, or thm:forward-KL-discrete formalized.

def cycle35DiscreteForwardKlEmFpMiddleObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle35_em_fp_middle"
  statement := "Maintain the cycle 35 middle source-to-Lean map for appendix.tex lines 260-385: use the compiled endpoint-vector lemmas and divergence-regrouping lemma as local algebra, while keeping stochastic endpoint laws, conditional drift density/measurability, the conditional-drift Fokker-Planck equation, Laplacian split, boundary integration by parts, and stitched regularity as explicit obligations."
  source := saldForwardKlDiscreteConditionalFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle35DiscreteForwardKlEmFpMiddleContract",
    "SALD.cycle35DiscreteForwardKlEmFpUpperPacket",
    "SALD.discreteForwardKlEmInterpolationLeftEndpointVector",
    "SALD.discreteForwardKlEmInterpolationRightEndpointVector",
    "SALD.discreteForwardKlConditionalFpDivergenceDriftSplit",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract",
    "SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract",
    "sald.discrete_forward_kl.em_endpoint_laws",
    "sald.discrete_forward_kl.conditional_drift_density",
    "sald.discrete_forward_kl.em_conditional_fokker_planck",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "sald.discrete_forward_kl.stitched_interval_regularity",
    "FokkerPlanckContract",
    "KLContract",
    "FIContract"
  ]
  note := "This middle obligation records proof-producing local algebra for the EM interpolation endpoint and conditional-FP regrouping only. It does not mark endpoint law matching, the conditional Fokker-Planck theorem, density/boundary regularity, KL derivative, LSI, DV, Gronwall, or thm:forward-KL-discrete formalized."