Samplinglib
Lean gate not recorded for this source state main · 0e31a3cda412

AutoSamplingTheory.SALD.cycle19DiscreteForwardKlAccumulatedErrorMiddleObligation

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 cycle19DiscreteForwardKlAccumulatedErrorMiddleObligation :
    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.cycle19_accumulated_error_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-19 middle source-to-Lean map for the discrete accumulated-error bridge: appendix lines 557-590 and main_body.tex lines 309-323 must route through the Gronwall output, linear-slowdown substitution, residual-exponent bound, endpoint rewrites, and A_alpha/barGamma/barDelta collection without changing the theorem statement or constants.
source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldForwardKlDiscreteAccumulatedErrorSource — 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.cycle19DiscreteForwardKlUpperPacket
  2. sald.discrete_forward_kl.gronwall_accumulation
  3. sald.discrete_forward_kl.linear_slowdown_specialization
  4. sald.discrete_forward_kl.residual_exponent_bound
  5. sald.discrete_forward_kl.accumulated_error_bridge
  6. sald.discrete_forward_kl.em_endpoint_laws
  7. sald.discrete_forward_kl.stitched_interval_regularity
  8. sald.discrete_forward_kl.coefficient_chain_audit
  9. sald.gronwall.integrating_factor
note : String (explicit)

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

cycle19DiscreteForwardKlMiddleContract is workflow/ledger data for the lower accumulated-error bridge. It does not prove thm:forward-KL-discrete, does not reopen EM/DV/frozen-defect subproofs, and does not promote Gronwall or interval-integral monotonicity.
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 cycle19DiscreteForwardKlAccumulatedErrorMiddleObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle19_accumulated_error_middle"
  statement := "Maintain the cycle-19 middle source-to-Lean map for the discrete accumulated-error bridge: appendix lines 557-590 and main_body.tex lines 309-323 must route through the Gronwall output, linear-slowdown substitution, residual-exponent bound, endpoint rewrites, and A_alpha/barGamma/barDelta collection without changing the theorem statement or constants."
  source := saldForwardKlDiscreteAccumulatedErrorSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle19DiscreteForwardKlUpperPacket",
    "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",
    "sald.discrete_forward_kl.coefficient_chain_audit",
    "sald.gronwall.integrating_factor"
  ]
  note := "cycle19DiscreteForwardKlMiddleContract is workflow/ledger data for the lower accumulated-error bridge. It does not prove thm:forward-KL-discrete, does not reopen EM/DV/frozen-defect subproofs, and does not promote Gronwall or interval-integral monotonicity."

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