AutoSamplingTheory.SALD.cycle51DiscreteForwardKlSkeletonObligation

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 cycle51DiscreteForwardKlSkeletonObligation : 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_theorem_interface_route

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 upper re-checks and wires thm:forward-KL-discrete after the cycle-50 continuous derivative/DV handoff: main_body.tex:299-323 stays fixed, appendix.tex:260-385 is consumed through the EM endpoint/conditional-Fokker-Planck interfaces, appendix.tex:388-491 through the discrete KL derivative with frozen defect and eq:LSI-KL-FI, appendix.tex:493-523 through the EM DV velocity witness, and appendix.tex:526-592 through Gronwall and the accumulated-error bridge. The EM/Fokker-Planck backend is used as a source-cited obligation interface, not reproved in this cycle.

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.cycle51DiscreteForwardKlSkeletonUpperPacket
2. SALD.cycle49MainSkeletonAnalyticReadinessObligation
3. SALD.cycle49MainSkeletonAnalyticMiddleObligation
4. SALD.cycle46DiscreteForwardKlSkeletonObligation
5. SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation
6. SALD.cycle50ForwardKlDerivativeLowerObligation
7. SALD.forwardKlDerivativeDvGronwallCoefficientOfKlFiVelocityScalingScalar
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.stitched_interval_regularity
14. sald.discrete_forward_kl.em_interpolation_fp
15. SALD.discreteForwardKlDerivativeCandidateContract
16. sald.discrete_forward_kl.kl_derivative
17. SALD.frozenDeltaCrossLipSaldContract
18. sald.discrete_forward_kl.frozen_delta_cross_lip
19. SALD.saldLsiKlFiDensityTestContract
20. probability.lsi_to_kl_fi
21. dvVariationalFormulaInterface saldDvVariationSource
22. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
23. sald.discrete_forward_kl.dv_finite_log_mgf_witness
24. sald.discrete_forward_kl.dv_velocity_bound
25. SALD.discreteForwardKlGronwallInstantiationContract
26. sald.discrete_forward_kl.gronwall_accumulation
27. SALD.discreteForwardKlAccumulatedErrorBridgeContract
28. sald.discrete_forward_kl.linear_slowdown_specialization
29. sald.discrete_forward_kl.residual_exponent_bound
30. sald.discrete_forward_kl.accumulated_error_bridge
31. sald.discrete_forward_kl.coefficient_chain_audit
32. lem:gronwall
33. lem:dv_variation
34. eq:LSI-KL-FI
35. thm:forward-KL

note : String (explicit)

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

This is an upper-role interface-route record, not an analytic proof. It adds no hidden EM, density, absolute-continuity, finite-log-mgf, endpoint, boundary, interval-integrability, or coefficient assumptions to thm:forward-KL-discrete.

def cycle51DiscreteForwardKlSkeletonObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle51_theorem_interface_route"
  statement := "Cycle 51 upper re-checks and wires thm:forward-KL-discrete after the cycle-50 continuous derivative/DV handoff: main_body.tex:299-323 stays fixed, appendix.tex:260-385 is consumed through the EM endpoint/conditional-Fokker-Planck interfaces, appendix.tex:388-491 through the discrete KL derivative with frozen defect and eq:LSI-KL-FI, appendix.tex:493-523 through the EM DV velocity witness, and appendix.tex:526-592 through Gronwall and the accumulated-error bridge. The EM/Fokker-Planck backend is used as a source-cited obligation interface, not reproved in this cycle."
  source := saldForwardKlDiscreteProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle51DiscreteForwardKlSkeletonUpperPacket",
    "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
    "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle46DiscreteForwardKlSkeletonObligation",
    "SALD.cycle46DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle50ForwardKlDerivativeLowerObligation",
    "SALD.forwardKlDerivativeDvGronwallCoefficientOfKlFiVelocityScalingScalar",
    "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.stitched_interval_regularity",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "SALD.discreteForwardKlDerivativeCandidateContract",
    "sald.discrete_forward_kl.kl_derivative",
    "SALD.frozenDeltaCrossLipSaldContract",
    "sald.discrete_forward_kl.frozen_delta_cross_lip",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "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.linear_slowdown_specialization",
    "sald.discrete_forward_kl.residual_exponent_bound",
    "sald.discrete_forward_kl.accumulated_error_bridge",
    "sald.discrete_forward_kl.coefficient_chain_audit",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "thm:forward-KL"
  ]
  note := "This is an upper-role interface-route record, not an analytic proof. It adds no hidden EM, density, absolute-continuity, finite-log-mgf, endpoint, boundary, interval-integrability, or coefficient assumptions to thm:forward-KL-discrete."

/-- Cycle-51 middle audit for the discrete forward-KL theorem route.

This is the middle-role synchronization layer for the current sprint.  It keeps
the upper theorem route fixed, records the appendix line map around the discrete
KL derivative backend, and selects lower work on `sald.discrete_forward_kl.kl_derivative`
without attempting to prove the EM conditional Fokker--Planck theorem here.
-/