AutoSamplingTheory.SALD.cycle50ForwardKlSkeletonObligation

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.

Lean statement of this data definition

The part after the colon is the output data type. This declaration takes no mathematical proof inputs.

def cycle50ForwardKlSkeletonObligation : 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.cycle50_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 50 upper re-checks and wires the faithful continuous thm:forward-KL skeleton after the cycle-49 readiness audit: main_body.tex:238-247 stays fixed, appendix.tex:168-228 routes through the continuous KL derivative/Fokker-Planck interface and eq:LSI-KL-FI, appendix.tex:230-241 routes through the DV finite-log-mgf witness and alpha-complexity interface, and appendix.tex:244-252 routes through lem:gronwall with endpoint and coefficient side conditions. The EM interpolation Fokker-Planck interface remains visible only as the downstream discrete slow backend.

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

SALD.cycle50ForwardKlSkeletonUpperPacket
SALD.cycle49MainSkeletonAnalyticReadinessObligation
SALD.cycle49MainSkeletonAnalyticMiddleObligation
SALD.cycle45ForwardKlSkeletonObligation
SALD.cycle45ForwardKlSkeletonMiddleObligation
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
dvVariationalFormulaInterface saldDvVariationSource
SALD.saldDvFiniteLogMgfContract
SALD.forwardKlDvFiniteLogMgfWitnessContract
sald.forward_kl.dv_finite_log_mgf_witness
sald.forward_kl.dv_energy_bound
SALD.saldGronwallEndpointCalculusContract
SALD.forwardKlGronwallInstantiationContract
SALD.forwardKlGronwallSideConditionContract
sald.forward_kl.endpoint_schedule_identities
sald.forward_kl.gronwall_application
sald.forward_kl.gronwall_side_conditions
SALD.discreteForwardKlEmInterpolationSideConditionContract
sald.discrete_forward_kl.em_interpolation_fp

note : String (explicit)

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

This is an upper-role route closure record, not an analytic proof. It preserves the source theorem statement and keeps all unresolved Gronwall, DV, LSI/KL/FI, KL-derivative, and EM interpolation backends below formalized status.

Exact Lean data construction

Each field assignment stores the corresponding value shown above. Omitted fields use the explicitly identified schema defaults. Strings that name theorems remain strings; they do not call those theorems.

def cycle50ForwardKlSkeletonObligation : ProofObligation where
  id := "sald.forward_kl.cycle50_theorem_skeleton_route"
  statement := "Cycle 50 upper re-checks and wires the faithful continuous thm:forward-KL skeleton after the cycle-49 readiness audit: main_body.tex:238-247 stays fixed, appendix.tex:168-228 routes through the continuous KL derivative/Fokker-Planck interface and eq:LSI-KL-FI, appendix.tex:230-241 routes through the DV finite-log-mgf witness and alpha-complexity interface, and appendix.tex:244-252 routes through lem:gronwall with endpoint and coefficient side conditions. The EM interpolation Fokker-Planck interface remains visible only as the downstream discrete slow backend."
  source := saldForwardKlProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle50ForwardKlSkeletonUpperPacket",
    "SALD.cycle49MainSkeletonAnalyticReadinessObligation",
    "SALD.cycle49MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle45ForwardKlSkeletonObligation",
    "SALD.cycle45ForwardKlSkeletonMiddleObligation",
    "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",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "SALD.forwardKlDvFiniteLogMgfWitnessContract",
    "sald.forward_kl.dv_finite_log_mgf_witness",
    "sald.forward_kl.dv_energy_bound",
    "SALD.saldGronwallEndpointCalculusContract",
    "SALD.forwardKlGronwallInstantiationContract",
    "SALD.forwardKlGronwallSideConditionContract",
    "sald.forward_kl.endpoint_schedule_identities",
    "sald.forward_kl.gronwall_application",
    "sald.forward_kl.gronwall_side_conditions",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  note := "This is an upper-role route closure record, not an analytic proof. It preserves the source theorem statement and keeps all unresolved Gronwall, DV, LSI/KL/FI, KL-derivative, and EM interpolation backends below formalized status."

/-- Cycle-50 middle audit for the continuous forward-KL theorem skeleton.

This is the middle-role synchronization layer after the cycle-49 readiness
audit and the cycle-50 upper route wrapper.  It keeps the theorem statement
fixed, checks the paper-order route, and selects the continuous KL
derivative/Fokker--Planck backend as the lower-ready theorem-level target.
-/

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