AutoSamplingTheory.SALD.discreteForwardKlCoefficientChainObligation

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 discreteForwardKlCoefficientChainObligation : 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.coefficient_chain_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.

Formalize the coefficient bookkeeping for thm:forward-KL-discrete from appendix lines 454-592 and main_body.tex lines 309-323: the two quarter-FI cross-term bounds, LSI conversion, DV velocity coefficient, s-to-t time change, Gronwall a(t), b(t), endpoint identifications, linear-slowdown collection of barGamma and barDelta, and the scalar side conditions listed by discreteForwardKlCoefficientChainAuditContract.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteCoefficientChainSource — 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.discrete_forward_kl.em_endpoint_laws
2. sald.discrete_forward_kl.stitched_interval_regularity
3. sald.discrete_forward_kl.frozen_delta_cross_lip
4. sald.discrete_forward_kl.kl_derivative
5. sald.discrete_forward_kl.dv_finite_log_mgf_witness
6. sald.discrete_forward_kl.dv_velocity_bound
7. SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar
8. sald.discrete_forward_kl.gronwall_accumulation
9. sald.discrete_forward_kl.linear_slowdown_specialization
10. sald.discrete_forward_kl.residual_exponent_bound
11. sald.discrete_forward_kl.accumulated_error_bridge
12. probability.lsi_to_kl_fi
13. probability.dv_variational_formula
14. sald.gronwall.integrating_factor

note : String (explicit)

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

discreteForwardKlCoefficientChainAuditContract keeps the one-step Gamma/Delta coefficients and accumulated-error constants aligned with the source theorem. SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar formalizes only the dot{s}*dot t^2 scalar rewrite under supplied inverse-schedule hypotheses; the audit remains an obligation, not an extra theorem assumption.

def discreteForwardKlCoefficientChainObligation : ProofObligation where
  id := "sald.discrete_forward_kl.coefficient_chain_audit"
  statement := "Formalize the coefficient bookkeeping for thm:forward-KL-discrete from appendix lines 454-592 and main_body.tex lines 309-323: the two quarter-FI cross-term bounds, LSI conversion, DV velocity coefficient, s-to-t time change, Gronwall a(t), b(t), endpoint identifications, linear-slowdown collection of barGamma and barDelta, and the scalar side conditions listed by discreteForwardKlCoefficientChainAuditContract."
  source := saldForwardKlDiscreteCoefficientChainSource
  status := ProofStatus.obligation
  dependsOn := [
    "sald.discrete_forward_kl.em_endpoint_laws",
    "sald.discrete_forward_kl.stitched_interval_regularity",
    "sald.discrete_forward_kl.frozen_delta_cross_lip",
    "sald.discrete_forward_kl.kl_derivative",
    "sald.discrete_forward_kl.dv_finite_log_mgf_witness",
    "sald.discrete_forward_kl.dv_velocity_bound",
    "SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar",
    "sald.discrete_forward_kl.gronwall_accumulation",
    "sald.discrete_forward_kl.linear_slowdown_specialization",
    "sald.discrete_forward_kl.residual_exponent_bound",
    "sald.discrete_forward_kl.accumulated_error_bridge",
    "probability.lsi_to_kl_fi",
    "probability.dv_variational_formula",
    "sald.gronwall.integrating_factor"
  ]
  note := "discreteForwardKlCoefficientChainAuditContract keeps the one-step Gamma/Delta coefficients and accumulated-error constants aligned with the source theorem. SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar formalizes only the dot{s}*dot t^2 scalar rewrite under supplied inverse-schedule hypotheses; the audit remains an obligation, not an extra theorem assumption."