AutoSamplingTheory.SALD.cycle23DiscreteForwardKlCoefficientChainMiddleObligation

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 cycle23DiscreteForwardKlCoefficientChainMiddleObligation : 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.cycle23_coefficient_chain_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-23 middle source-to-Lean map for thm:forward-KL-discrete: appendix.tex lines 454-553 must be audited as the first coefficient-chain lower slice, including the two quarter-FI cross-term bounds, LSI conversion, DV dot t(s)^2*alpha^(-1) coefficient, and the s-to-t rewrite to dot{s}(t)^(-1)*alpha^(-1), while appendix.tex lines 557-590 and main_body.tex lines 309-323 remain the separate accumulated-error bridge.

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.cycle23DiscreteForwardKlUpperPacket
2. SALD.discreteForwardKlCoefficientChainAuditContract
3. sald.discrete_forward_kl.coefficient_chain_audit
4. sald.discrete_forward_kl.frozen_delta_cross_lip
5. sald.discrete_forward_kl.kl_derivative
6. sald.discrete_forward_kl.dv_finite_log_mgf_witness
7. sald.discrete_forward_kl.dv_velocity_bound
8. SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar
9. sald.discrete_forward_kl.gronwall_accumulation
10. sald.discrete_forward_kl.linear_slowdown_specialization
11. sald.discrete_forward_kl.residual_exponent_bound
12. sald.discrete_forward_kl.accumulated_error_bridge
13. sald.discrete_forward_kl.em_endpoint_laws
14. sald.discrete_forward_kl.stitched_interval_regularity
15. probability.lsi_to_kl_fi
16. probability.dv_variational_formula
17. sald.gronwall.integrating_factor

note : String (explicit)

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

cycle23DiscreteForwardKlMiddleContract is workflow/ledger data for the lower coefficient-chain audit. The compiled SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar covers only scalar real algebra after inverse-schedule side conditions are supplied; it does not prove thm:forward-KL-discrete, does not change Gamma/Delta/barGamma/barDelta or the alpha ranges, and does not promote LSI, DV, Gronwall, EM Fokker-Planck, or the omitted frozen-defect proof.

def cycle23DiscreteForwardKlCoefficientChainMiddleObligation : ProofObligation where
  id := "sald.discrete_forward_kl.cycle23_coefficient_chain_middle"
  statement := "Maintain the cycle-23 middle source-to-Lean map for thm:forward-KL-discrete: appendix.tex lines 454-553 must be audited as the first coefficient-chain lower slice, including the two quarter-FI cross-term bounds, LSI conversion, DV dot t(s)^2*alpha^(-1) coefficient, and the s-to-t rewrite to dot{s}(t)^(-1)*alpha^(-1), while appendix.tex lines 557-590 and main_body.tex lines 309-323 remain the separate accumulated-error bridge."
  source := saldForwardKlDiscreteCoefficientChainSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle23DiscreteForwardKlUpperPacket",
    "SALD.discreteForwardKlCoefficientChainAuditContract",
    "sald.discrete_forward_kl.coefficient_chain_audit",
    "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",
    "sald.discrete_forward_kl.em_endpoint_laws",
    "sald.discrete_forward_kl.stitched_interval_regularity",
    "probability.lsi_to_kl_fi",
    "probability.dv_variational_formula",
    "sald.gronwall.integrating_factor"
  ]
  note := "cycle23DiscreteForwardKlMiddleContract is workflow/ledger data for the lower coefficient-chain audit. The compiled SALD.discreteForwardKlTimeChangeSquareCoefficientRewriteScalar covers only scalar real algebra after inverse-schedule side conditions are supplied; it does not prove thm:forward-KL-discrete, does not change Gamma/Delta/barGamma/barDelta or the alpha ranges, and does not promote LSI, DV, Gronwall, EM Fokker-Planck, or the omitted frozen-defect proof."