AutoSamplingTheory.SALD.cycle57GuidedGeneralSkeletonObligation

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 cycle57GuidedGeneralSkeletonObligation : 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.guided_general.cycle57_upper_route

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 57 upper records that cycle 56 passed cleanly and needs no recovery, then rechecks appendix.tex:619-951 at theorem level: prop:guided_path_residual is consumed through the guided normalizer and centered residual identity; thm:general-moving-target-SALD is consumed through the general Fokker-Planck/KL derivative, eq:LSI-KL-FI, residual DV finite-log-mgf and positive-alpha witnesses, lem:gronwall endpoint/exponent side conditions, and the pure-contraction residual-zero obligation. Broad cited-theory backfill remains deferred; the selected lower packet is sald.general_moving_target.kl_derivative over appendix.tex:765-884.

source : AutoSamplingTheory.SourceAnchor (explicit)

SourceAnchor supporting the intended requirement.

AutoSamplingTheory.SALD.saldGeneralMovingTargetSource — 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.cycle57GuidedGeneralSkeletonUpperPacket
SALD.cycle56DiscreteForwardKlSkeletonObligation
SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
SALD.cycle52GuidedGeneralSkeletonObligation
SALD.cycle52GuidedGeneralSkeletonMiddleObligation
SALD.cycle52GuidedGeneralDerivativeDvLowerObligation
SALD.cycle54MainSkeletonAnalyticInterfaceObligation
SALD.cycle54MainSkeletonAnalyticMiddleObligation
SALD.guidedResidualIdentityContract
sald.guided_path_residual.normalizer_derivative
sald.guided_path_residual.identity
SALD.generalMovingTargetStatementContract
SALD.generalMovingTargetDerivativeCandidateContract
SALD.generalMovingTargetDerivativeObligation
sald.general_moving_target.kl_derivative
SALD.generalMovingTargetPostYoungDerivativeBoundScalar
SALD.generalMovingTargetLsiDerivativeBoundScalar
SALD.generalMovingTargetTimeChangedDerivativeBoundScalar
SALD.generalMovingTargetPreDvDerivativeBoundScalar
SALD.saldLsiKlFiDensityTestContract
probability.lsi_to_kl_fi
dvVariationalFormulaInterface saldDvVariationSource
SALD.saldDvFiniteLogMgfContract
SALD.generalMovingTargetDvFiniteLogMgfWitnessContract
SALD.generalMovingTargetDvPositiveAlphaScalingContract
sald.general_moving_target.dv_finite_log_mgf_witness
sald.general_moving_target.dv_positive_alpha_scaling
sald.general_moving_target.dv_m_energy
SALD.saldGronwallEndpointCalculusContract
SALD.generalMovingTargetGronwallInstantiationContract
SALD.generalMovingTargetGronwallSideConditionContract
sald.general_moving_target.gronwall_application
sald.general_moving_target.gronwall_side_conditions
sald.general_moving_target.pure_contraction
SALD.discreteForwardKlEmInterpolationSideConditionContract
SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
sald.general_moving_target_discrete.em_interpolation_fp
lem:gronwall
lem:dv_variation
eq:LSI-KL-FI
def:alpha-complexity

note : String (explicit)

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

This is an upper workflow obligation and route check, not analytic backfill. It adds no hidden assumptions and does not promote Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL differentiation, EM interpolation, guided residual, or the continuous general theorem.

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 cycle57GuidedGeneralSkeletonObligation : ProofObligation where
  id := "sald.guided_general.cycle57_upper_route"
  statement := "Cycle 57 upper records that cycle 56 passed cleanly and needs no recovery, then rechecks appendix.tex:619-951 at theorem level: prop:guided_path_residual is consumed through the guided normalizer and centered residual identity; thm:general-moving-target-SALD is consumed through the general Fokker-Planck/KL derivative, eq:LSI-KL-FI, residual DV finite-log-mgf and positive-alpha witnesses, lem:gronwall endpoint/exponent side conditions, and the pure-contraction residual-zero obligation. Broad cited-theory backfill remains deferred; the selected lower packet is sald.general_moving_target.kl_derivative over appendix.tex:765-884."
  source := saldGeneralMovingTargetSource
  status := ProofStatus.obligation
  dependsOn := [
    "SALD.cycle57GuidedGeneralSkeletonUpperPacket",
    "SALD.cycle56DiscreteForwardKlSkeletonObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle52GuidedGeneralSkeletonObligation",
    "SALD.cycle52GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle52GuidedGeneralDerivativeDvLowerObligation",
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
    "SALD.guidedResidualIdentityContract",
    "sald.guided_path_residual.normalizer_derivative",
    "sald.guided_path_residual.identity",
    "SALD.generalMovingTargetStatementContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.generalMovingTargetDerivativeObligation",
    "sald.general_moving_target.kl_derivative",
    "SALD.generalMovingTargetPostYoungDerivativeBoundScalar",
    "SALD.generalMovingTargetLsiDerivativeBoundScalar",
    "SALD.generalMovingTargetTimeChangedDerivativeBoundScalar",
    "SALD.generalMovingTargetPreDvDerivativeBoundScalar",
    "SALD.saldLsiKlFiDensityTestContract",
    "probability.lsi_to_kl_fi",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldDvFiniteLogMgfContract",
    "SALD.generalMovingTargetDvFiniteLogMgfWitnessContract",
    "SALD.generalMovingTargetDvPositiveAlphaScalingContract",
    "sald.general_moving_target.dv_finite_log_mgf_witness",
    "sald.general_moving_target.dv_positive_alpha_scaling",
    "sald.general_moving_target.dv_m_energy",
    "SALD.saldGronwallEndpointCalculusContract",
    "SALD.generalMovingTargetGronwallInstantiationContract",
    "SALD.generalMovingTargetGronwallSideConditionContract",
    "sald.general_moving_target.gronwall_application",
    "sald.general_moving_target.gronwall_side_conditions",
    "sald.general_moving_target.pure_contraction",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  note := "This is an upper workflow obligation and route check, not analytic backfill. It adds no hidden assumptions and does not promote Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL differentiation, EM interpolation, guided residual, or the continuous general theorem."

/-- Cycle-57 middle audit for the guided residual and continuous general
moving-target theorem route.

This is the middle-role source-to-Lean synchronization layer for the cycle-57
upper route.  It verifies the appendix proof order, keeps every slow analytic
dependency in an already named interface, and selects the continuous general
KL derivative backend for lower work without changing any paper statement.
-/

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