AutoSamplingTheory.SALD.cycle46DiscreteForwardKlSkeletonObligation

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 cycle46DiscreteForwardKlSkeletonObligation : 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.cycle46_theorem_skeleton_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 46 upper wires the source-cited analytic interfaces into thm:forward-KL-discrete: the EM endpoint and conditional-Fokker-Planck interface supplies the interpolated law and derivative setup; the discrete KL derivative block uses the frozen score-defect lemma and eq:LSI-KL-FI; lem:dv_variation with the EM finite-log-mgf witness supplies the velocity-energy bound; lem:gronwall with stitched-interval regularity gives the appendix general-schedule bound; the linear-slowdown bridge recovers exactly the main_body.tex:309-323 display with barGamma and barDelta. All slow analytic interfaces remain obligation or source-cited.

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.cycle44MainSkeletonAnalyticInterfaceObligation
2. SALD.cycle46DiscreteForwardKlSkeletonUpperPacket
3. SALD.discreteForwardKlStatementContract
4. SALD.discreteForwardKlEmInterpolationSideConditionContract
5. sald.discrete_forward_kl.em_endpoint_laws
6. sald.discrete_forward_kl.em_conditional_fokker_planck
7. sald.discrete_forward_kl.stitched_interval_regularity
8. sald.discrete_forward_kl.em_interpolation_fp
9. SALD.discreteForwardKlDerivativeCandidateContract
10. sald.discrete_forward_kl.kl_derivative
11. SALD.frozenDeltaCrossLipSaldContract
12. sald.discrete_forward_kl.frozen_delta_cross_lip
13. SALD.saldLsiKlFiDensityTestContract
14. probability.lsi_to_kl_fi
15. SALD.discreteForwardKlDvFiniteLogMgfWitnessContract
16. sald.discrete_forward_kl.dv_finite_log_mgf_witness
17. sald.discrete_forward_kl.dv_velocity_bound
18. SALD.discreteForwardKlGronwallInstantiationContract
19. sald.discrete_forward_kl.gronwall_accumulation
20. SALD.discreteForwardKlAccumulatedErrorBridgeContract
21. sald.discrete_forward_kl.linear_slowdown_specialization
22. sald.discrete_forward_kl.residual_exponent_bound
23. sald.discrete_forward_kl.accumulated_error_bridge
24. sald.discrete_forward_kl.coefficient_chain_audit
25. lem:gronwall
26. lem:dv_variation
27. eq:LSI-KL-FI
28. thm:forward-KL

note : String (explicit)

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

This is a theorem-route wrapper for main skeleton sprint 3. It does not add hidden smoothness, endpoint, density, finite-log-mgf, interval-integrability, or coefficient assumptions to thm:forward-KL-discrete.

def cycle46DiscreteForwardKlSkeletonObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle46_theorem_skeleton_route"
  statement := "Cycle 46 upper wires the source-cited analytic interfaces into thm:forward-KL-discrete: the EM endpoint and conditional-Fokker-Planck interface supplies the interpolated law and derivative setup; the discrete KL derivative block uses the frozen score-defect lemma and eq:LSI-KL-FI; lem:dv_variation with the EM finite-log-mgf witness supplies the velocity-energy bound; lem:gronwall with stitched-interval regularity gives the appendix general-schedule bound; the linear-slowdown bridge recovers exactly the main_body.tex:309-323 display with barGamma and barDelta. All slow analytic interfaces remain obligation or source-cited."
  source := saldForwardKlDiscreteProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle46DiscreteForwardKlSkeletonUpperPacket",
    "SALD.discreteForwardKlStatementContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "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.discreteForwardKlDerivativeCandidateContract",
    "sald.discrete_forward_kl.kl_derivative",
    "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.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 a theorem-route wrapper for main skeleton sprint 3. It does not add hidden smoothness, endpoint, density, finite-log-mgf, interval-integrability, or coefficient assumptions to thm:forward-KL-discrete."

/-- Cycle-46 proof-DAG pane for the discrete forward-KL theorem route. -/