AutoSamplingTheory.SALD.cycle45ForwardKlSkeletonMiddleObligation

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 cycle45ForwardKlSkeletonMiddleObligation : 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.forward_kl.cycle45_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 45 middle audits the continuous thm:forward-KL theorem skeleton after the upper wrapper: main_body.tex:238-247 is kept unchanged, appendix.tex:168-252 is routed through the named continuous KL derivative, LSI/KL/FI, DV finite-log-mgf, and Gronwall endpoint/exponent interfaces in paper order, and the next lower target is the theorem-level Gronwall side-condition backend sald.forward_kl.gronwall_side_conditions. All slow analytic interfaces remain obligation or source-cited.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlProofSource — 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.cycle45ForwardKlSkeletonUpperPacket
3. SALD.cycle45ForwardKlSkeletonObligation
4. SALD.cycle45ForwardKlSkeletonMiddleContract
5. SALD.continuousForwardKlStatementContract
6. SALD.forwardKlDerivativeCandidateContract
7. SALD.forwardKlDerivativeSideConditionContract
8. sald.forward_kl.density_boundary_regular
9. sald.forward_kl.schedule_time_change
10. sald.forward_kl.kl_derivative
11. SALD.saldLsiKlFiDensityTestContract
12. probability.lsi_to_kl_fi
13. SALD.forwardKlDvFiniteLogMgfWitnessContract
14. sald.forward_kl.dv_finite_log_mgf_witness
15. sald.forward_kl.dv_energy_bound
16. SALD.forwardKlGronwallInstantiationContract
17. SALD.forwardKlGronwallSideConditionContract
18. sald.forward_kl.gronwall_side_conditions
19. sald.forward_kl.gronwall_application
20. SALD.discreteForwardKlEmInterpolationSideConditionContract

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 smoothness, density, endpoint, absolute-continuity, finite-log-mgf, or interval-integrability assumptions to thm:forward-KL.

def cycle45ForwardKlSkeletonMiddleObligation : ProofObligation where
  id := "sald.forward_kl.cycle45_middle_route_audit"
  statement := "Cycle 45 middle audits the continuous thm:forward-KL theorem skeleton after the upper wrapper: main_body.tex:238-247 is kept unchanged, appendix.tex:168-252 is routed through the named continuous KL derivative, LSI/KL/FI, DV finite-log-mgf, and Gronwall endpoint/exponent interfaces in paper order, and the next lower target is the theorem-level Gronwall side-condition backend sald.forward_kl.gronwall_side_conditions. All slow analytic interfaces remain obligation or source-cited."
  source := saldForwardKlProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle44MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle45ForwardKlSkeletonUpperPacket",
    "SALD.cycle45ForwardKlSkeletonObligation",
    "SALD.cycle45ForwardKlSkeletonMiddleContract",
    "SALD.continuousForwardKlStatementContract",
    "SALD.forwardKlDerivativeCandidateContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "sald.forward_kl.density_boundary_regular",
    "sald.forward_kl.schedule_time_change",
    "sald.forward_kl.kl_derivative",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "SALD.forwardKlDvFiniteLogMgfWitnessContract",
    "sald.forward_kl.dv_finite_log_mgf_witness",
    "sald.forward_kl.dv_energy_bound",
    "SALD.forwardKlGronwallInstantiationContract",
    "SALD.forwardKlGronwallSideConditionContract",
    "sald.forward_kl.gronwall_side_conditions",
    "sald.forward_kl.gronwall_application",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract"
  ]
  note := "This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It does not add hidden smoothness, density, endpoint, absolute-continuity, finite-log-mgf, or interval-integrability assumptions to thm:forward-KL."

/-- Cycle-50 upper packet for the continuous forward-KL theorem skeleton.

After the cycle-49 post-route readiness audit, this packet re-enters the
specific continuous `thm:forward-KL` route.  It records the upper-role check
that the five slow analytic interfaces are precise enough to be consumed by
the theorem skeleton, while keeping the theorem contract-only.
-/