AutoSamplingTheory.SALD.cycle35DiscreteForwardKlEmFpUpperObligation

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 cycle35DiscreteForwardKlEmFpUpperObligation : 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_upper

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 upper proof-closure packet for appendix.tex lines 260-385: after the Gronwall, DV, LSI/KL/FI, and continuous forward-KL derivative proof-sprint slices, middle/lower should translate the EM interpolation endpoint laws and conditional-drift Fokker--Planck backend into a proof-producing endpoint or conditional-drift interface before any frozen-defect, DV, Gronwall, or accumulated-error work.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteInterpolationSource — 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.cycle35DiscreteForwardKlEmFpUpperPacket
2. SALD.cycle15DiscreteForwardKlUpperPacket
3. SALD.cycle15DiscreteForwardKlMiddleContract
4. SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract
5. SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract
6. SALD.discreteForwardKlEmInterpolationSideConditionContract
7. sald.discrete_forward_kl.em_endpoint_laws
8. sald.discrete_forward_kl.conditional_drift_density
9. sald.discrete_forward_kl.em_conditional_fokker_planck
10. sald.discrete_forward_kl.em_interpolation_fp
11. FokkerPlanckContract
12. KLContract
13. FIContract

note : String (explicit)

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

This is an upper workflow obligation, not a proof. It fixes the lower target to the existing EM endpoint and conditional-FP interfaces, preserves thm:forward-KL-discrete and all source constants, and keeps the analytic Fokker-Planck theorem below formalized status until a compiled local proof or precise source-cited interface replaces it.

def cycle35DiscreteForwardKlEmFpUpperObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle35_em_fp_upper"
  statement := "Maintain the cycle 35 upper proof-closure packet for appendix.tex lines 260-385: after the Gronwall, DV, LSI/KL/FI, and continuous forward-KL derivative proof-sprint slices, middle/lower should translate the EM interpolation endpoint laws and conditional-drift Fokker--Planck backend into a proof-producing endpoint or conditional-drift interface before any frozen-defect, DV, Gronwall, or accumulated-error work."
  source := saldForwardKlDiscreteInterpolationSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle35DiscreteForwardKlEmFpUpperPacket",
    "SALD.cycle15DiscreteForwardKlUpperPacket",
    "SALD.cycle15DiscreteForwardKlMiddleContract",
    "SALD.cycle15DiscreteForwardKlEmConditionalFpLowerContract",
    "SALD.cycle15DiscreteForwardKlConditionalDriftDensityContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "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",
    "FokkerPlanckContract",
    "KLContract",
    "FIContract"
  ]
  note := "This is an upper workflow obligation, not a proof. It fixes the lower target to the existing EM endpoint and conditional-FP interfaces, preserves thm:forward-KL-discrete and all source constants, and keeps the analytic Fokker-Planck theorem below formalized status until a compiled local proof or precise source-cited interface replaces it."