AutoSamplingTheory.SALD.cycle51DiscreteForwardKlSkeletonMiddleObligation

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 cycle51DiscreteForwardKlSkeletonMiddleObligation : 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.cycle51_middle_route_audit

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 51 middle audits the discrete thm:forward-KL-discrete route after the upper interface wrapper: main_body.tex:299-323 remains unchanged, appendix.tex:334-491 is selected as the next derivative backend, and appendix.tex:334-385 EM endpoint/conditional-Fokker-Planck interfaces are consumed explicitly as source-cited obligations rather than reproved. The follow-on DV, Gronwall, stitched-interval, residual-exponent, and accumulated-error interfaces remain separate obligations.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteDerivativeSource — 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.cycle51DiscreteForwardKlSkeletonUpperPacket
2. SALD.cycle51DiscreteForwardKlSkeletonObligation
3. SALD.cycle51DiscreteForwardKlSkeletonMiddleContract
4. SALD.cycle49MainSkeletonAnalyticReadinessObligation
5. SALD.cycle49MainSkeletonAnalyticMiddleObligation
6. SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation
7. SALD.cycle50ForwardKlDerivativeLowerObligation
8. SALD.discreteForwardKlStatementContract
9. SALD.discreteForwardKlEmInterpolationSideConditionContract
10. sald.discrete_forward_kl.em_endpoint_laws
11. sald.discrete_forward_kl.conditional_drift_density
12. sald.discrete_forward_kl.em_conditional_fokker_planck
13. sald.discrete_forward_kl.em_interpolation_fp
14. SALD.discreteForwardKlDerivativeCandidateContract
15. SALD.discreteForwardKlDerivativeObligation
16. SALD.frozenDeltaCrossLipSaldContract
17. sald.discrete_forward_kl.frozen_delta_cross_lip
18. SALD.saldLsiKlFiDensityTestContract
19. probability.lsi_to_kl_fi
20. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
21. sald.discrete_forward_kl.dv_finite_log_mgf_witness
22. sald.discrete_forward_kl.dv_velocity_bound
23. SALD.discreteForwardKlGronwallInstantiationContract
24. sald.discrete_forward_kl.gronwall_accumulation
25. SALD.discreteForwardKlAccumulatedErrorBridgeContract
26. sald.discrete_forward_kl.accumulated_error_bridge
27. lem:gronwall
28. lem:dv_variation
29. eq:LSI-KL-FI

note : String (explicit)

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

This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It does not add hidden endpoint, density, absolute-continuity, finite-log-mgf, conditional-law, boundary, stitched-interval, or coefficient assumptions to thm:forward-KL-discrete.

def cycle51DiscreteForwardKlSkeletonMiddleObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle51_middle_route_audit"
  statement := "Cycle 51 middle audits the discrete thm:forward-KL-discrete route after the upper interface wrapper: main_body.tex:299-323 remains unchanged, appendix.tex:334-491 is selected as the next derivative backend, and appendix.tex:334-385 EM endpoint/conditional-Fokker-Planck interfaces are consumed explicitly as source-cited obligations rather than reproved. The follow-on DV, Gronwall, stitched-interval, residual-exponent, and accumulated-error interfaces remain separate obligations."
  source := saldForwardKlDiscreteDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle51DiscreteForwardKlSkeletonUpperPacket",
    "SALD.cycle51DiscreteForwardKlSkeletonObligation",
    "SALD.cycle51DiscreteForwardKlSkeletonMiddleContract",
    "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
    "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle50ForwardKlDerivativeLowerObligation",
    "SALD.discreteForwardKlStatementContract",
    "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",
    "SALD.discreteForwardKlDerivativeCandidateContract",
    "SALD.discreteForwardKlDerivativeObligation",
    "SALD.frozenDeltaCrossLipSaldContract",
    "sald.discrete_forward_kl.frozen_delta_cross_lip",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "SALD.discreteForwardKlDvFiniteLogMgfWitnessContract",
    "sald.discrete_forward_kl.dv_finite_log_mgf_witness",
    "sald.discrete_forward_kl.dv_velocity_bound",
    "SALD.discreteForwardKlGronwallInstantiationContract",
    "sald.discrete_forward_kl.gronwall_accumulation",
    "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
    "sald.discrete_forward_kl.accumulated_error_bridge",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI"
  ]
  note := "This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It does not add hidden endpoint, density, absolute-continuity, finite-log-mgf, conditional-law, boundary, stitched-interval, or coefficient assumptions to thm:forward-KL-discrete."

/-- Cycle-32 upper packet for the DV proof-closure sprint.

This packet explicitly checks the proof-closure order and selects
`lem:dv_variation` only after the cycle-31 reviewer left `lem:gronwall` as a
partial local proof with remaining endpoint/integrability obligations.  The
DV result is cited by the paper, so this cycle narrows the source-cited
interface and lower handoff without upgrading it to a local Lean theorem.
-/