AutoSamplingTheory.SALD.cycle26ForwardKlDvWitnessMiddleObligation

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 cycle26ForwardKlDvWitnessMiddleObligation : 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.cycle26_dv_witness_middle

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Maintain the cycle 26 middle source-to-Lean map for appendix.tex lines 230-241 and main_body.tex lines 218-248: classify the DV witness side conditions for nu=rho_{s(t)}, mu=pi_t, and Z=alpha*||v_t||^2 as common-space/absolute-continuity, measurability, alpha0-to-alpha finite-log-mgf, and positive-alpha scaling obligations before the DV-energy inequality is attempted.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDvEnergySource — 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.cycle26ForwardKlUpperPacket
SALD.cycle26ForwardKlMiddleContract
SALD.forwardKlDvFiniteLogMgfWitnessContract
SALD.forwardKlDvFiniteLogMgfWitnessObligation
SALD.forwardKlDvAlphaMonotonicityContract
SALD.saldDvFiniteLogMgfContract
probability.dv_variational_formula
sald.dv_variation.finite_log_mgf_interface
sald.forward_kl.dv_alpha_mgf_monotonicity
SALD.forwardKlDvPositiveAlphaScalingScalar
SALD.forwardKlDvPositiveAlphaCoefficientScalar
sald.forward_kl.dv_finite_log_mgf_witness
sald.forward_kl.moving_target_dependency_chain

note : String (explicit)

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

This is a middle-role source-dependency audit for the selected lower target. It keeps the DV formula source-cited, leaves alpha0-to-alpha monotonicity and measure interfaces as obligations, and does not add theorem assumptions or prove 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 cycle26ForwardKlDvWitnessMiddleObligation : ProofObligation where
  id := "sald.forward_kl.cycle26_dv_witness_middle"
  statement := "Maintain the cycle 26 middle source-to-Lean map for appendix.tex lines 230-241 and main_body.tex lines 218-248: classify the DV witness side conditions for nu=rho_{s(t)}, mu=pi_t, and Z=alpha*||v_t||^2 as common-space/absolute-continuity, measurability, alpha0-to-alpha finite-log-mgf, and positive-alpha scaling obligations before the DV-energy inequality is attempted."
  source := saldForwardKlDvEnergySource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle26ForwardKlUpperPacket",
    "SALD.cycle26ForwardKlMiddleContract",
    "SALD.forwardKlDvFiniteLogMgfWitnessContract",
    "SALD.forwardKlDvFiniteLogMgfWitnessObligation",
    "SALD.forwardKlDvAlphaMonotonicityContract",
    "SALD.saldDvFiniteLogMgfContract",
    "probability.dv_variational_formula",
    "sald.dv_variation.finite_log_mgf_interface",
    "sald.forward_kl.dv_alpha_mgf_monotonicity",
    "SALD.forwardKlDvPositiveAlphaScalingScalar",
    "SALD.forwardKlDvPositiveAlphaCoefficientScalar",
    "sald.forward_kl.dv_finite_log_mgf_witness",
    "sald.forward_kl.moving_target_dependency_chain"
  ]
  note := "This is a middle-role source-dependency audit for the selected lower target. It keeps the DV formula source-cited, leaves alpha0-to-alpha monotonicity and measure interfaces as obligations, and does not add theorem assumptions or prove thm:forward-KL."

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