AutoSamplingTheory.SALD.cycle15DiscreteForwardKlEmConditionalFpLowerObligation

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 cycle15DiscreteForwardKlEmConditionalFpLowerObligation : 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.cycle15_conditional_fp_lower_packet

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-15 lower-ready line ledger for appendix lines 347-385: bar b_{k,s}, the conditional law/density interface of hat X_s, the conditional-drift Fokker--Planck equation, the Laplacian split relative to tilde pi_s, and the handoff into the KL derivative block.

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.cycle15DiscreteForwardKlMiddleContract
2. SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract
3. SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract
4. sald.discrete_forward_kl.conditional_drift_density
5. sald.discrete_forward_kl.em_conditional_fokker_planck
6. sald.discrete_forward_kl.em_endpoint_laws
7. FokkerPlanckContract
8. KLContract
9. FIContract

note : String (explicit)

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

This is a lower packet and line ledger, not a theorem proof. It keeps endpoint stitching, the frozen Gamma/Delta lemma, DV velocity, Gronwall, and accumulated-error collection outside the conditional Fokker--Planck slice.

def cycle15DiscreteForwardKlEmConditionalFpLowerObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle15_conditional_fp_lower_packet"
  statement := "Maintain the cycle-15 lower-ready line ledger for appendix lines 347-385: bar b_{k,s}, the conditional law/density interface of hat X_s, the conditional-drift Fokker--Planck equation, the Laplacian split relative to tilde pi_s, and the handoff into the KL derivative block."
  source := saldForwardKlDiscreteConditionalFpSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle15DiscreteForwardKlMiddleContract",
    "SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract",
    "SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract",
    "sald.discrete_forward_kl.conditional_drift_density",
    "sald.discrete_forward_kl.em_conditional_fokker_planck",
    "sald.discrete_forward_kl.em_endpoint_laws",
    "FokkerPlanckContract",
    "KLContract",
    "FIContract"
  ]
  note := "This is a lower packet and line ledger, not a theorem proof. It keeps endpoint stitching, the frozen Gamma/Delta lemma, DV velocity, Gronwall, and accumulated-error collection outside the conditional Fokker--Planck slice."