Samplinglib

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AutoSamplingTheory.SALD.cycle64MainSkeletonAnalyticInterfaceLedger

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.SALD.MainSkeletonAnalyticInterfaceLedger. 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 cycle64MainSkeletonAnalyticInterfaceLedger :
    MainSkeletonAnalyticInterfaceLedger

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.

sourceBlock : AutoSamplingTheory.SourceAnchor (explicit)

Nested provenance data.

AutoSamplingTheory.SALD.saldGeneralMovingTargetDiscreteDerivativeSource — audited data reference, not expanded and not a compiled dependency edge

objective : String (explicit)

Descriptive text even when field names say formula, theorem, inequality, derivative, source gap, or proof.

Cycle 64 upper: cycle 63 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for exactly one narrow cited-theory/SDE backend backfill, not broad reusable API work; the single lower packet that best reduces risk is the EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387, because it supports both thm:forward-KL-discrete and thm:general-moving-target-SALD-discrete.

sourceLabels : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

lem:gronwall
lem:dv_variation
eq:LSI-KL-FI
proof:thm:forward-KL:derivative
proof:thm:forward-KL-discrete:conditional-fp
proof:thm:general-moving-target-SALD:derivative
proof:thm:general-moving-target-SALD-discrete:derivative
thm:forward-KL
thm:forward-KL-discrete
prop:guided_path_residual
thm:general-moving-target-SALD
thm:unified-forward-KL
thm:general-moving-target-SALD-discrete

analyticInterfaces : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

Gronwall: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, and the cycle-36/41 assembled wrappers expose continuous a,b, endpoint-safe differentiability or right-derivative/FTC semantics, interval-integrability, endpoint evaluation, exponent algebra, and theorem-specific coefficient/display side conditions; lem:gronwall remains ProofStatus.obligation.
Donsker-Varadhan: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific DV witness contracts expose common-space probability measures, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, positive-alpha scaling, and E_alpha rewriting; the Boucheron variational equality remains ProofStatus.sourceCited.
LSI/KL/FI: SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, probability.lsi_to_kl_fi, and the cycle-43 density/entropy/Fisher helpers expose rho << pi, Radon-Nikodym density, zero-set convention, admissible sqrt-density test or approximation, entropy identity, finite KL/FI, and the Fisher chain rule; eq:LSI-KL-FI remains ProofStatus.obligation.
Continuous Fokker-Planck/KL derivative: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and cycle-60/62 scalar handoffs expose mass conservation, KL differentiation under the integral, SALD/general Fokker-Planck equations, integration by parts, target transport, residual scaling, LSI, and inverse-schedule calculus; analytic derivative backends remain ProofStatus.obligation.
Euler-Maruyama interpolation Fokker-Planck: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, cycle-63 endpoint-law Measure.map helpers, and sald.general_moving_target_discrete.em_interpolation_fp expose endpoint laws, common-space bookkeeping, regular conditional drift, density/absolute-continuity, weak conditional Fokker-Planck signs, Laplacian split, and stitched intervals; the conditional-law/FP backend remains ProofStatus.obligation.

theoremRoute : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

1. thm:forward-KL is wired through continuous KL derivative/Fokker-Planck, eq:LSI-KL-FI, DV velocity-energy, endpoint schedule identities, and Gronwall side conditions.
2. thm:forward-KL-discrete is wired through EM endpoint/conditional-FP, frozen defect, LSI, DV velocity, Gronwall accumulation, and accumulated-error display interfaces.
3. prop:guided_path_residual is wired through normalizer differentiation, guided-density differentiation, divergence cancellation, and mean-zero residual obligations; it is not promoted by this ledger.
4. thm:general-moving-target-SALD is wired through continuous general KL derivative/Fokker-Planck, residual Young/LSI, residual DV, sigma-weighted Gronwall, endpoint/exponent side conditions, and pure-contraction specialization.
5. thm:unified-forward-KL remains the appendix specialization of thm:general-moving-target-SALD through prop:guided_path_residual, the correction-field transport bridge, c_t=u_t, and m_t=w_t.
6. thm:general-moving-target-SALD-discrete is wired through general EM endpoint/conditional-FP, frozen-delta, KL derivative/LSI, residual DV, constant-schedule time change, Gronwall/display stitching, and the guided discrete specialization.

modeDiscipline : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

faithfulPaper Phase 1: use only main_body.tex, appendix.tex, and iteration_complexity.tex under the original SALD paper root; sald_version_2.tex remains excluded.
Keep all source theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, and proof order fixed.
Every unproved analytic backend remains ProofStatus.obligation or ProofStatus.sourceCited; already compiled scalar and endpoint-law helpers are local dependencies only.
Only one cited-theory/SDE backend may be pursued after this upper ledger, and it must be theorem-route useful.

nonGoals : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

No source-index rebaseline beyond the required acceptance command unless a reviewer reports a blocking anchor defect.
No broad SLT import, Gaussian concentration port, entropy-duality library reorganization, disintegration project, or teaching API rewrite.
No hidden endpoint, density, absolute-continuity, finite-KL/FI, finite-log-mgf, boundary, smoothness, conditional-law, sigma-positivity, schedule, coefficient-regularity, or stitched-interval assumption is added to a source theorem statement.
No alternate proof route replaces derivative -> LSI -> DV -> Gronwall, the correction-field specialization, or the paper EM/frozen-delta route.

lowerPacket : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

Middle should synchronize this cycle-64 analytic-interface ledger with conversion-windows/ASTIS-SALD-001.md and proof-obligations/ASTIS-SALD-001.md, preserving the theorem route order forward-KL, discrete forward-KL, guided residual, general moving-target, unified forward-KL, discrete general moving-target.
Lower should target exactly SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation / SALD.generalMovingTargetDiscreteDerivativeSideConditionContract / sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.
First sub-slice: after the cycle-63 endpoint-law helpers, expose common probability space data, hat rho_s and tilde pi_s density/absolute-continuity, and endpoint-law stitching assumptions needed before KL differentiation.
Second sub-slice: define and typecheck the regular conditional drift bar b_{k,s}(x), including measurability and integrability hypotheses for the conditional expectation in appendix.tex:1364-1371.
Third sub-slice: state the weak conditional Fokker-Planck equation from appendix.tex:1372-1387 with the exact source signs for the drift divergence and sigma_eta^2/2 Laplacian.
Do not promote endpoint Measure.map bookkeeping into conditional drift, density, weak Fokker-Planck, KL derivative, DV, LSI/KL/FI, or Gronwall formalization.

reviewerChecklist : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

SALD.cycle64MainSkeletonAnalyticInterfaceObligation is listed by all six theorem contracts while those contracts remain ProofStatus.contractOnly.
SALD.forwardKlProofDag, SALD.discreteForwardKlProofDag, SALD.generalVaSaldProofDag, and SALD.generalVaSaldDiscreteProofDag include SALD.cycle64MainSkeletonAnalyticInterfaceDag.
SALD.saldDependenciesForLabel includes cycle64MainSkeletonDependencyNames for the five slow interfaces and the six theorem-route labels.
The lower packet is the EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387, not a new theorem statement, theorem status promotion, or broad SLT/SDE port.
Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL differentiation, EM conditional-FP, theorem contracts, and SLT reuse statuses all remain below formalized unless already compiled locally.
python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass.

dependencies : List String (explicit)

Ordered descriptive/naming checklist, not logical conjunction or compiler dependency list.

Ordered data items

SALD.cycle63UnifiedDiscreteGeneralMiddleObligation
SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation
SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation
SALD.cycle60ForwardKlSkeletonMiddleObligation
SALD.cycle59MainSkeletonAnalyticInterfaceObligation
SALD.saldGronwallEndpointCalculusContract
dvVariationalFormulaInterface saldDvVariationSource
SALD.saldLsiKlFiDensityTestContract
SALD.forwardKlDerivativeSideConditionContract
SALD.generalMovingTargetDerivativeCandidateContract
SALD.discreteForwardKlEmInterpolationSideConditionContract
SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation
SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation

status : AutoSamplingTheory.ProofStatus (explicit)

Stored workflow tag; honor the exact default but do not infer mathematical certification.

AutoSamplingTheory.ProofStatus.obligation — stored label only; no proof certification

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 cycle64MainSkeletonAnalyticInterfaceLedger :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteDerivativeSource
  objective := "Cycle 64 upper: cycle 63 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for exactly one narrow cited-theory/SDE backend backfill, not broad reusable API work; the single lower packet that best reduces risk is the EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387, because it supports both thm:forward-KL-discrete and thm:general-moving-target-SALD-discrete."
  sourceLabels := [
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "proof:thm:forward-KL:derivative",
    "proof:thm:forward-KL-discrete:conditional-fp",
    "proof:thm:general-moving-target-SALD:derivative",
    "proof:thm:general-moving-target-SALD-discrete:derivative",
    "thm:forward-KL",
    "thm:forward-KL-discrete",
    "prop:guided_path_residual",
    "thm:general-moving-target-SALD",
    "thm:unified-forward-KL",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Gronwall: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, and the cycle-36/41 assembled wrappers expose continuous a,b, endpoint-safe differentiability or right-derivative/FTC semantics, interval-integrability, endpoint evaluation, exponent algebra, and theorem-specific coefficient/display side conditions; lem:gronwall remains ProofStatus.obligation.",
    "Donsker-Varadhan: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific DV witness contracts expose common-space probability measures, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, positive-alpha scaling, and E_alpha rewriting; the Boucheron variational equality remains ProofStatus.sourceCited.",
    "LSI/KL/FI: SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, probability.lsi_to_kl_fi, and the cycle-43 density/entropy/Fisher helpers expose rho << pi, Radon-Nikodym density, zero-set convention, admissible sqrt-density test or approximation, entropy identity, finite KL/FI, and the Fisher chain rule; eq:LSI-KL-FI remains ProofStatus.obligation.",
    "Continuous Fokker-Planck/KL derivative: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and cycle-60/62 scalar handoffs expose mass conservation, KL differentiation under the integral, SALD/general Fokker-Planck equations, integration by parts, target transport, residual scaling, LSI, and inverse-schedule calculus; analytic derivative backends remain ProofStatus.obligation.",
    "Euler-Maruyama interpolation Fokker-Planck: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, cycle-63 endpoint-law Measure.map helpers, and sald.general_moving_target_discrete.em_interpolation_fp expose endpoint laws, common-space bookkeeping, regular conditional drift, density/absolute-continuity, weak conditional Fokker-Planck signs, Laplacian split, and stitched intervals; the conditional-law/FP backend remains ProofStatus.obligation."
  ]
  theoremRoute := [
    "1. thm:forward-KL is wired through continuous KL derivative/Fokker-Planck, eq:LSI-KL-FI, DV velocity-energy, endpoint schedule identities, and Gronwall side conditions.",
    "2. thm:forward-KL-discrete is wired through EM endpoint/conditional-FP, frozen defect, LSI, DV velocity, Gronwall accumulation, and accumulated-error display interfaces.",
    "3. prop:guided_path_residual is wired through normalizer differentiation, guided-density differentiation, divergence cancellation, and mean-zero residual obligations; it is not promoted by this ledger.",
    "4. thm:general-moving-target-SALD is wired through continuous general KL derivative/Fokker-Planck, residual Young/LSI, residual DV, sigma-weighted Gronwall, endpoint/exponent side conditions, and pure-contraction specialization.",
    "5. thm:unified-forward-KL remains the appendix specialization of thm:general-moving-target-SALD through prop:guided_path_residual, the correction-field transport bridge, c_t=u_t, and m_t=w_t.",
    "6. thm:general-moving-target-SALD-discrete is wired through general EM endpoint/conditional-FP, frozen-delta, KL derivative/LSI, residual DV, constant-schedule time change, Gronwall/display stitching, and the guided discrete specialization."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: use only main_body.tex, appendix.tex, and iteration_complexity.tex under the original SALD paper root; sald_version_2.tex remains excluded.",
    "Keep all source theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, and proof order fixed.",
    "Every unproved analytic backend remains ProofStatus.obligation or ProofStatus.sourceCited; already compiled scalar and endpoint-law helpers are local dependencies only.",
    "Only one cited-theory/SDE backend may be pursued after this upper ledger, and it must be theorem-route useful."
  ]
  nonGoals := [
    "No source-index rebaseline beyond the required acceptance command unless a reviewer reports a blocking anchor defect.",
    "No broad SLT import, Gaussian concentration port, entropy-duality library reorganization, disintegration project, or teaching API rewrite.",
    "No hidden endpoint, density, absolute-continuity, finite-KL/FI, finite-log-mgf, boundary, smoothness, conditional-law, sigma-positivity, schedule, coefficient-regularity, or stitched-interval assumption is added to a source theorem statement.",
    "No alternate proof route replaces derivative -> LSI -> DV -> Gronwall, the correction-field specialization, or the paper EM/frozen-delta route."
  ]
  lowerPacket := [
    "Middle should synchronize this cycle-64 analytic-interface ledger with conversion-windows/ASTIS-SALD-001.md and proof-obligations/ASTIS-SALD-001.md, preserving the theorem route order forward-KL, discrete forward-KL, guided residual, general moving-target, unified forward-KL, discrete general moving-target.",
    "Lower should target exactly SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation / SALD.generalMovingTargetDiscreteDerivativeSideConditionContract / sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.",
    "First sub-slice: after the cycle-63 endpoint-law helpers, expose common probability space data, hat rho_s and tilde pi_s density/absolute-continuity, and endpoint-law stitching assumptions needed before KL differentiation.",
    "Second sub-slice: define and typecheck the regular conditional drift bar b_{k,s}(x), including measurability and integrability hypotheses for the conditional expectation in appendix.tex:1364-1371.",
    "Third sub-slice: state the weak conditional Fokker-Planck equation from appendix.tex:1372-1387 with the exact source signs for the drift divergence and sigma_eta^2/2 Laplacian.",
    "Do not promote endpoint Measure.map bookkeeping into conditional drift, density, weak Fokker-Planck, KL derivative, DV, LSI/KL/FI, or Gronwall formalization."
  ]
  reviewerChecklist := [
    "SALD.cycle64MainSkeletonAnalyticInterfaceObligation is listed by all six theorem contracts while those contracts remain ProofStatus.contractOnly.",
    "SALD.forwardKlProofDag, SALD.discreteForwardKlProofDag, SALD.generalVaSaldProofDag, and SALD.generalVaSaldDiscreteProofDag include SALD.cycle64MainSkeletonAnalyticInterfaceDag.",
    "SALD.saldDependenciesForLabel includes cycle64MainSkeletonDependencyNames for the five slow interfaces and the six theorem-route labels.",
    "The lower packet is the EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387, not a new theorem statement, theorem status promotion, or broad SLT/SDE port.",
    "Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL differentiation, EM conditional-FP, theorem contracts, and SLT reuse statuses all remain below formalized unless already compiled locally.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle63UnifiedDiscreteGeneralMiddleObligation",
    "SALD.cycle63UnifiedDiscreteGeneralMeasureBackfillObligation",
    "SALD.cycle61DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle60ForwardKlSkeletonMiddleObligation",
    "SALD.cycle59MainSkeletonAnalyticInterfaceObligation",
    "SALD.saldGronwallEndpointCalculusContract",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMeasureMapOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteEmJointEndpointMarginalLawsOfNamedInterpolation"
  ]
  status := ProofStatus.obligation

/-- Cycle-64 upper obligation for the refreshed analytic-interface ledger. -/

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