AutoSamplingTheory.SALD.cycle62GuidedGeneralScaledResidualLowerObligation

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 cycle62GuidedGeneralScaledResidualLowerObligation : 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.general_moving_target.cycle62_scaled_residual_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 62 lower compiles the appendix.tex:813-835 scalar sign/scale handoff inside sald.general_moving_target.kl_derivative: after the target transport equation supplies tilde v_s=dot{t}(s)*v_{t(s)}, the c_t drift and v_t target-transport pairings, and the residual pairing m_t=v_t-c_t, SALD.generalMovingTargetKlDerivativeScaledResidualDisplayScalar rewrites the KL derivative display as -(sigma_{t(s)}^2/2)*FI - dot{t}(s)*int rho_s <m_{t(s)},A_s>. The analytic target-transport, integration-by-parts, density, mass-conservation, LSI, Young, and schedule backends remain obligations.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDerivativeSource — 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.cycle62GuidedGeneralSkeletonMiddleContract
SALD.cycle62GuidedGeneralSkeletonMiddleObligation
SALD.generalMovingTargetDerivativeCandidateContract
SALD.generalMovingTargetDerivativeObligation
SALD.generalMovingTargetKlDerivativeScaledResidualDisplayScalar
SALD.generalMovingTargetKlDerivativeResidualSplitScalar
sald.general_moving_target.kl_derivative
TransportVelocityContract
FokkerPlanckContract
KLContract
FIContract
sald.forward_kl.density_boundary_regular

note : String (explicit)

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

Formalized local Real algebra only. It preserves the source residual sign and dot{t}(s) scaling, and does not promote the continuous Fokker-Planck/KL derivative backend or thm:general-moving-target-SALD.

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 cycle62GuidedGeneralScaledResidualLowerObligation : ProofObligation where
  id := "sald.general_moving_target.cycle62_scaled_residual_lower"
  statement := "Cycle 62 lower compiles the appendix.tex:813-835 scalar sign/scale handoff inside sald.general_moving_target.kl_derivative: after the target transport equation supplies tilde v_s=dot{t}(s)*v_{t(s)}, the c_t drift and v_t target-transport pairings, and the residual pairing m_t=v_t-c_t, SALD.generalMovingTargetKlDerivativeScaledResidualDisplayScalar rewrites the KL derivative display as -(sigma_{t(s)}^2/2)*FI - dot{t}(s)*int rho_s <m_{t(s)},A_s>. The analytic target-transport, integration-by-parts, density, mass-conservation, LSI, Young, and schedule backends remain obligations."
  source := saldGeneralMovingTargetDerivativeSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle62GuidedGeneralSkeletonMiddleContract",
    "SALD.cycle62GuidedGeneralSkeletonMiddleObligation",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.generalMovingTargetDerivativeObligation",
    "SALD.generalMovingTargetKlDerivativeScaledResidualDisplayScalar",
    "SALD.generalMovingTargetKlDerivativeResidualSplitScalar",
    "sald.general_moving_target.kl_derivative",
    "TransportVelocityContract",
    "FokkerPlanckContract",
    "KLContract",
    "FIContract",
    "sald.forward_kl.density_boundary_regular"
  ]
  note := "Formalized local Real algebra only. It preserves the source residual sign and dot{t}(s) scaling, and does not promote the continuous Fokker-Planck/KL derivative backend or thm:general-moving-target-SALD."

/-- Cycle-62 proof-DAG pane for the guided/general upper route. -/

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