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

AutoSamplingTheory.SALD.cycle27DiscreteForwardKlAccumulatedCollectionUpperObligation

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 cycle27DiscreteForwardKlAccumulatedCollectionUpperObligation :
    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.cycle27_accumulated_collection_upper
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-27 upper packet for thm:forward-KL-discrete: after the coefficient-chain audit, the next lower target is the accumulated-error bridge from appendix lines 557-590 to main_body.tex lines 309-323, with endpoint rewrites, the linear-slowdown exponent split, and A_alpha/barGamma/barDelta collection kept separate from the frozen-defect, DV, LSI, and time-change subproofs.
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.cycle27DiscreteForwardKlUpperPacket
  2. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  3. sald.discrete_forward_kl.accumulated_error_bridge
  4. sald.discrete_forward_kl.linear_slowdown_specialization
  5. sald.discrete_forward_kl.residual_exponent_bound
  6. SALD.discreteForwardKlResidualExponentBoundScalar
  7. SALD.discreteForwardKlResidualExpBoundScalar
  8. SALD.discreteForwardKlAlphaComplexityCollectionScalar
  9. SALD.discreteForwardKlDeltaAccumulationScalar
  10. SALD.discreteForwardKlAccumulatedErrorCollectionScalar
  11. sald.discrete_forward_kl.coefficient_chain_audit
  12. sald.discrete_forward_kl.em_endpoint_laws
  13. sald.discrete_forward_kl.stitched_interval_regularity
  14. sald.gronwall.integrating_factor
note : String (explicit)

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

This is workflow/ledger data for the upper handoff. It does not prove thm:forward-KL-discrete, does not change the main-body constants, and does not promote Gronwall, interval-integral monotonicity, endpoint stitching, or the accumulated-error bridge beyond obligation status.
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 cycle27DiscreteForwardKlAccumulatedCollectionUpperObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle27_accumulated_collection_upper"
  statement := "Maintain the cycle-27 upper packet for thm:forward-KL-discrete: after the coefficient-chain audit, the next lower target is the accumulated-error bridge from appendix lines 557-590 to main_body.tex lines 309-323, with endpoint rewrites, the linear-slowdown exponent split, and A_alpha/barGamma/barDelta collection kept separate from the frozen-defect, DV, LSI, and time-change subproofs."
  source := saldForwardKlDiscreteAccumulatedErrorSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle27DiscreteForwardKlUpperPacket",
    "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
    "sald.discrete_forward_kl.accumulated_error_bridge",
      "sald.discrete_forward_kl.linear_slowdown_specialization",
      "sald.discrete_forward_kl.residual_exponent_bound",
      "SALD.discreteForwardKlResidualExponentBoundScalar",
      "SALD.discreteForwardKlResidualExpBoundScalar",
      "SALD.discreteForwardKlAlphaComplexityCollectionScalar",
      "SALD.discreteForwardKlDeltaAccumulationScalar",
      "SALD.discreteForwardKlAccumulatedErrorCollectionScalar",
      "sald.discrete_forward_kl.coefficient_chain_audit",
      "sald.discrete_forward_kl.em_endpoint_laws",
      "sald.discrete_forward_kl.stitched_interval_regularity",
    "sald.gronwall.integrating_factor"
  ]
  note := "This is workflow/ledger data for the upper handoff. It does not prove thm:forward-KL-discrete, does not change the main-body constants, and does not promote Gronwall, interval-integral monotonicity, endpoint stitching, or the accumulated-error bridge beyond obligation status."

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