AutoSamplingTheory.SALD.cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation

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 cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation :
    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.cycle66_accumulated_display_lower

statement : String (explicit)

Desired mathematical or workflow content as String; it is not a proposition in Prop and the def does not prove it.

Cycle 66 lower compiles SALD.discreteForwardKlMainDisplayBoundScalar for the final scalar/order wrapper in thm:forward-KL-discrete: once Gronwall supplies the initial term plus residual bound, the initial exponent split and residual-display wrapper produce exactly the main_body.tex:309-323 two-term display with exp(-r*int C_LSI)*exp(T/(r*alpha)+2*r*eta^2*barGamma/alpha')*KL(rho_0||pi_0) plus the same positive exponential times ((1/r)*A_alpha(pi,v)+2*r*eta*barDelta_{alpha'}).

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

SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation
SALD.discreteForwardKlAccumulatedErrorBridgeContract
SALD.discreteForwardKlAccumulatedErrorBridgeObligation
SALD.discreteForwardKlGronwallInitialExponentSplitScalar
SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces
SALD.discreteForwardKlResidualIntegralDisplayBoundScalar
SALD.discreteForwardKlMainDisplayBoundScalar
SALD.discreteForwardKlAccumulatedErrorCollectionScalar
SALD.discreteForwardKlAlphaComplexityCollectionScalar
SALD.discreteForwardKlDeltaAccumulationScalar
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

note : String (explicit)

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

Proof-producing scalar wrapper plus obligation only. It preserves the theorem target, source constants, and source labels. It does not prove EM/Fokker-Planck, endpoint stitching, Gronwall, residual-exponent monotonicity, barGamma/barDelta source identifications, or thm:forward-KL-discrete.

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 cycle66DiscreteForwardKlAccumulatedDisplayLowerObligation :
    ProofObligation where
  id := "sald.discrete_forward_kl.cycle66_accumulated_display_lower"
  statement := "Cycle 66 lower compiles SALD.discreteForwardKlMainDisplayBoundScalar for the final scalar/order wrapper in thm:forward-KL-discrete: once Gronwall supplies the initial term plus residual bound, the initial exponent split and residual-display wrapper produce exactly the main_body.tex:309-323 two-term display with exp(-r*int C_LSI)*exp(T/(r*alpha)+2*r*eta^2*barGamma/alpha')*KL(rho_0||pi_0) plus the same positive exponential times ((1/r)*A_alpha(pi,v)+2*r*eta*barDelta_{alpha'})."
  source := saldForwardKlDiscreteAccumulatedErrorSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.discreteForwardKlAccumulatedErrorBridgeContract",
    "SALD.discreteForwardKlAccumulatedErrorBridgeObligation",
    "SALD.discreteForwardKlGronwallInitialExponentSplitScalar",
    "SALD.discreteForwardKlGronwallInitialExponentSplitOfPieces",
    "SALD.discreteForwardKlResidualIntegralDisplayBoundScalar",
    "SALD.discreteForwardKlMainDisplayBoundScalar",
    "SALD.discreteForwardKlAccumulatedErrorCollectionScalar",
    "SALD.discreteForwardKlAlphaComplexityCollectionScalar",
    "SALD.discreteForwardKlDeltaAccumulationScalar",
    "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"
  ]
  note := "Proof-producing scalar wrapper plus obligation only. It preserves the theorem target, source constants, and source labels. It does not prove EM/Fokker-Planck, endpoint stitching, Gronwall, residual-exponent monotonicity, barGamma/barDelta source identifications, or thm:forward-KL-discrete."

/-- Cycle-66 proof-DAG pane for the post-cycle-65 discrete forward-KL skeleton
route. -/

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