AutoSamplingTheory.SALD.cycle15DiscreteForwardKlMiddleEmSpineObligation

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 cycle15DiscreteForwardKlMiddleEmSpineObligation : 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_middle_em_spine

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 middle source-to-Lean map for thm:forward-KL-discrete: appendix lines 260-590 must route through the EM endpoint laws, conditional-drift Fokker--Planck slice, stitched-interval regularity, frozen one-step defect, DV velocity witness, Gronwall accumulation, and accumulated-error bridge without changing the source theorem or constants.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteProofSource — 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.cycle15DiscreteForwardKlUpperPacket
2. sald.discrete_forward_kl.em_endpoint_laws
3. sald.discrete_forward_kl.em_conditional_fokker_planck
4. sald.discrete_forward_kl.stitched_interval_regularity
5. sald.discrete_forward_kl.em_interpolation_fp
6. sald.discrete_forward_kl.frozen_delta_cross_lip
7. sald.discrete_forward_kl.kl_derivative
8. sald.discrete_forward_kl.dv_finite_log_mgf_witness
9. sald.discrete_forward_kl.gronwall_accumulation
10. sald.discrete_forward_kl.accumulated_error_bridge

note : String (explicit)

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

This middle packet narrows the cycle-15 lower handoff to sald.discrete_forward_kl.em_conditional_fokker_planck while preserving endpoint/stitching, one-step Gamma/Delta, DV, Gronwall, and accumulated-error obligations as separate proof targets.

def cycle15DiscreteForwardKlMiddleEmSpineObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle15_middle_em_spine"
  statement := "Maintain the cycle-15 middle source-to-Lean map for thm:forward-KL-discrete: appendix lines 260-590 must route through the EM endpoint laws, conditional-drift Fokker--Planck slice, stitched-interval regularity, frozen one-step defect, DV velocity witness, Gronwall accumulation, and accumulated-error bridge without changing the source theorem or constants."
  source := saldForwardKlDiscreteProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle15DiscreteForwardKlUpperPacket",
    "sald.discrete_forward_kl.em_endpoint_laws",
    "sald.discrete_forward_kl.em_conditional_fokker_planck",
    "sald.discrete_forward_kl.stitched_interval_regularity",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "sald.discrete_forward_kl.frozen_delta_cross_lip",
    "sald.discrete_forward_kl.kl_derivative",
    "sald.discrete_forward_kl.dv_finite_log_mgf_witness",
    "sald.discrete_forward_kl.gronwall_accumulation",
    "sald.discrete_forward_kl.accumulated_error_bridge"
  ]
  note := "This middle packet narrows the cycle-15 lower handoff to sald.discrete_forward_kl.em_conditional_fokker_planck while preserving endpoint/stitching, one-step Gamma/Delta, DV, Gronwall, and accumulated-error obligations as separate proof targets."