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

AutoSamplingTheory.SALD.cycle27DiscreteForwardKlAccumulatedCollectionMiddleObligation

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 cycle27DiscreteForwardKlAccumulatedCollectionMiddleObligation :
    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_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-27 middle source-to-Lean map for thm:forward-KL-discrete: the lower-ready accumulated-error sub-slice is endpointBridge plus alphaComplexityCollection and deltaAccumulation from appendix lines 557-590 to main_body.tex lines 309-323, while residual-exponent monotonicity, barGamma identification, endpoint stitching, and Gronwall remain separate obligations.
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.cycle27DiscreteForwardKlMiddleContract
  3. SALD.discreteForwardKlAccumulatedErrorBridgeContract
  4. sald.discrete_forward_kl.accumulated_error_bridge
  5. sald.discrete_forward_kl.linear_slowdown_specialization
  6. sald.discrete_forward_kl.residual_exponent_bound
  7. SALD.discreteForwardKlResidualExponentBoundScalar
  8. SALD.discreteForwardKlResidualExpBoundScalar
  9. SALD.discreteForwardKlAlphaComplexityCollectionScalar
  10. SALD.discreteForwardKlDeltaAccumulationScalar
  11. SALD.discreteForwardKlAccumulatedErrorCollectionScalar
  12. sald.discrete_forward_kl.coefficient_chain_audit
  13. sald.discrete_forward_kl.gronwall_accumulation
  14. sald.discrete_forward_kl.em_endpoint_laws
  15. sald.discrete_forward_kl.stitched_interval_regularity
  16. def:alpha-complexity
  17. sald.gronwall.integrating_factor
note : String (explicit)

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

This middle packet is workflow/ledger data for lower work on the accumulated-error bridge. It does not prove thm:forward-KL-discrete, does not change Gamma, Delta, barGamma, barDelta, alpha, alpha', eta, or r, and does not promote Gronwall, DV, LSI-to-KL/FI, endpoint stitching, interval-integral monotonicity, or the bridge itself 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 cycle27DiscreteForwardKlAccumulatedCollectionMiddleObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle27_accumulated_collection_middle"
  statement := "Maintain the cycle-27 middle source-to-Lean map for thm:forward-KL-discrete: the lower-ready accumulated-error sub-slice is endpointBridge plus alphaComplexityCollection and deltaAccumulation from appendix lines 557-590 to main_body.tex lines 309-323, while residual-exponent monotonicity, barGamma identification, endpoint stitching, and Gronwall remain separate obligations."
  source := saldForwardKlDiscreteAccumulatedErrorSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle27DiscreteForwardKlUpperPacket",
    "SALD.cycle27DiscreteForwardKlMiddleContract",
    "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.gronwall_accumulation",
    "sald.discrete_forward_kl.em_endpoint_laws",
    "sald.discrete_forward_kl.stitched_interval_regularity",
    "def:alpha-complexity",
    "sald.gronwall.integrating_factor"
  ]
  note := "This middle packet is workflow/ledger data for lower work on the accumulated-error bridge. It does not prove thm:forward-KL-discrete, does not change Gamma, Delta, barGamma, barDelta, alpha, alpha', eta, or r, and does not promote Gronwall, DV, LSI-to-KL/FI, endpoint stitching, interval-integral monotonicity, or the bridge itself beyond obligation status."

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