AutoSamplingTheory.SALD.cycle65ForwardKlSkeletonMiddleObligation

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 cycle65ForwardKlSkeletonMiddleObligation : 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.cycle65_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 65 middle audits the post-cycle-64 continuous thm:forward-KL skeleton: main_body.tex:238-247 remains unchanged, appendix.tex:168-252 is consumed in paper order through the continuous KL derivative/Fokker-Planck interface, eq:LSI-KL-FI, lem:dv_variation, and lem:gronwall, the downstream EM interpolation backend remains visible only for discrete reuse, and the next proof-producing lower packet stays exactly sald.forward_kl.kl_derivative over appendix.tex:168-228. All theorem statuses and slow analytic interfaces remain below formalized.

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.cycle65ForwardKlSkeletonUpperPacket
SALD.cycle65ForwardKlSkeletonObligation
SALD.cycle65ForwardKlSkeletonMiddleContract
SALD.cycle64MainSkeletonAnalyticInterfaceObligation
SALD.cycle64MainSkeletonAnalyticMiddleObligation
SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation
SALD.cycle60ForwardKlSkeletonObligation
SALD.cycle60ForwardKlSkeletonMiddleObligation
SALD.cycle60ForwardKlDerivativeRawLowerObligation
SALD.cycle55ForwardKlSkeletonMiddleObligation
SALD.cycle50ForwardKlDerivativeLowerObligation
SALD.continuousForwardKlStatementContract
SALD.forwardKlDerivativeCandidateContract
SALD.forwardKlDerivativeSideConditionContract
SALD.forwardKlDerivativeObligation
SALD.forwardKlDensityBoundaryObligation
SALD.forwardKlScheduleTimeChangeObligation
SALD.forwardKlPreDvDerivativeBoundOfRawKlFiVelocityScalingScalar
SALD.forwardKlPointwisePreDvDerivativeBoundOfRawKlFiVelocityScaling
SALD.cycle65ForwardKlDerivativePointwiseLowerObligation
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_side_conditions
sald.forward_kl.gronwall_application
SALD.discreteForwardKlEmInterpolationSideConditionContract
sald.discrete_forward_kl.em_interpolation_fp
lem:gronwall
lem:dv_variation
eq:LSI-KL-FI
def:alpha-complexity

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 adds no hidden density, boundary, endpoint, absolute-continuity, finite-log-mgf, finite-KL/FI, schedule, coefficient-regularity, or EM conditional-law assumptions to thm:forward-KL.

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 cycle65ForwardKlSkeletonMiddleObligation : ProofObligation where
  id := "sald.forward_kl.cycle65_middle_route_audit"
  statement := "Cycle 65 middle audits the post-cycle-64 continuous thm:forward-KL skeleton: main_body.tex:238-247 remains unchanged, appendix.tex:168-252 is consumed in paper order through the continuous KL derivative/Fokker-Planck interface, eq:LSI-KL-FI, lem:dv_variation, and lem:gronwall, the downstream EM interpolation backend remains visible only for discrete reuse, and the next proof-producing lower packet stays exactly sald.forward_kl.kl_derivative over appendix.tex:168-228. All theorem statuses and slow analytic interfaces remain below formalized."
  source := saldForwardKlProofSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle65ForwardKlSkeletonUpperPacket",
    "SALD.cycle65ForwardKlSkeletonObligation",
    "SALD.cycle65ForwardKlSkeletonMiddleContract",
    "SALD.cycle64MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle64MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle64GeneralMovingTargetDiscreteConditionalDriftLowerObligation",
    "SALD.cycle60ForwardKlSkeletonObligation",
    "SALD.cycle60ForwardKlSkeletonMiddleObligation",
    "SALD.cycle60ForwardKlDerivativeRawLowerObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleObligation",
    "SALD.cycle50ForwardKlDerivativeLowerObligation",
    "SALD.continuousForwardKlStatementContract",
    "SALD.forwardKlDerivativeCandidateContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.forwardKlDerivativeObligation",
    "SALD.forwardKlDensityBoundaryObligation",
    "SALD.forwardKlScheduleTimeChangeObligation",
    "SALD.forwardKlPreDvDerivativeBoundOfRawKlFiVelocityScalingScalar",
    "SALD.forwardKlPointwisePreDvDerivativeBoundOfRawKlFiVelocityScaling",
    "SALD.cycle65ForwardKlDerivativePointwiseLowerObligation",
    "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_side_conditions",
    "sald.forward_kl.gronwall_application",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "This is a middle workflow obligation and source-to-Lean route audit, not an analytic proof. It adds no hidden density, boundary, endpoint, absolute-continuity, finite-log-mgf, finite-KL/FI, schedule, coefficient-regularity, or EM conditional-law assumptions to thm:forward-KL."

/-- Cycle-65 lower proof-producing obligation for the pointwise continuous
derivative wrapper. -/

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