AutoSamplingTheory.SALD.cycle54MainSkeletonAnalyticInterfaceLedger

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.

def cycle54MainSkeletonAnalyticInterfaceLedger :
    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 54 upper: re-run the main skeleton sprint-1 analytic interface ledger after cycles 50-53, check the five slow source-cited interfaces against all six theorem skeletons, and keep the next lower packet on the discrete general EM conditional-law/Fokker-Planck and KL-derivative backend.

sourceLabels : List String (explicit)

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

Ordered data items

1. lem:gronwall
2. lem:dv_variation
3. eq:LSI-KL-FI
4. proof:thm:forward-KL:derivative
5. proof:thm:forward-KL-discrete:conditional-fp
6. proof:thm:general-moving-target-SALD:derivative
7. proof:thm:general-moving-target-SALD-discrete:derivative
8. thm:forward-KL
9. thm:forward-KL-discrete
10. prop:guided_path_residual
11. thm:general-moving-target-SALD
12. thm:unified-forward-KL
13. thm:general-moving-target-SALD-discrete

analyticInterfaces : List String (explicit)

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

Ordered data items

1. Gronwall interface: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, the cycle-36/41 assembly wrappers, and theorem-specific Gronwall side-condition contracts expose closed-interval differentiability semantics, FTC/order integration, coefficient interval-integrability, endpoint evaluation, and exponent rewrites; lem:gronwall remains ProofStatus.obligation.
2. DV interface: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific velocity/residual finite-log-mgf witness contracts expose same-space probability measures, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, alpha-range and positive-alpha scaling; the Boucheron variational equality remains ProofStatus.sourceCited.
3. LSI/KL/FI interface: SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, and the cycle-43 density/entropy plus integral Fisher-chain helpers expose rho << pi, Radon-Nikodym density, zero-set convention, admissible sqrt-density test or approximation, entropy identity, finite KL/FI, and Fisher chain rule; probability.lsi_to_kl_fi remains ProofStatus.obligation.
4. Continuous forward-KL/general Fokker-Planck/KL derivative interface: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and the cycle-50/52 scalar handoffs expose mass conservation, KL differentiation under the integral, SALD/general Fokker-Planck equations, target transport, integration by parts, LSI handoff, and inverse-schedule calculus; the analytic derivative backends remain ProofStatus.obligation.
5. Euler-Maruyama interpolation Fokker-Planck interface: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation, SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation, and SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff expose endpoint laws, named-law pushforward bookkeeping, regular conditional drift, density/absolute-continuity, weak conditional Fokker-Planck, Laplacian split, stitched intervals, and common-space assumptions; only endpoint-law congruence and the sigma-weighted divergence regrouping are formalized.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. thm:forward-KL consumes the continuous KL derivative, LSI/KL/FI, DV velocity witness, endpoint schedule, and Gronwall side-condition interfaces from appendix.tex:168-252 and main_body.tex:238-247.
2. 2. thm:forward-KL-discrete consumes the EM endpoint/conditional-FP backend, frozen-defect estimate, LSI, DV velocity witness, stitched Gronwall, and accumulated-error bridge from appendix.tex:260-592 and main_body.tex:299-323.
3. 3. prop:guided_path_residual consumes only the normalizer derivative, guided-path differentiation, divergence cancellation, and mean-zero residual interfaces from appendix.tex:619-704; it remains the upstream input to the unified specialization.
4. 4. thm:general-moving-target-SALD consumes the continuous general derivative, residual Young/LSI, residual DV, sigma-weighted Gronwall, endpoint/exponent side conditions, and pure-contraction obligations from appendix.tex:724-949.
5. 5. thm:unified-forward-KL remains the paper specialization of thm:general-moving-target-SALD using prop:guided_path_residual and eq:poisson-eq, with no direct alternate KL proof.
6. 6. thm:general-moving-target-SALD-discrete consumes the general EM endpoint/conditional-FP backend, frozen-delta lemma, discrete KL derivative/LSI, residual DV, constant-schedule time change, and Gronwall stitching from appendix.tex:1313-1603.

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1: preserve main_body.tex, appendix.tex, and iteration_complexity.tex as the only source files; sald_version_2.tex remains excluded.
2. Do not change theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, or proof routes.
3. All unproved analytic backends stay obligation or sourceCited; only already compiled local scalar algebra and endpoint-law congruence helpers may be marked formalized.
4. The next lower packet must improve a theorem-consumed backend interface, not start broad SLT/SDE backfill or a detached scalar lemma.

nonGoals : List String (explicit)

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

Ordered data items

1. No source-index rebaseline beyond the acceptance command.
2. No imported SLT theorem is marked formalized for DV, LSI, concentration, disintegration, or one-step EM analysis.
3. No endpoint, density, absolute-continuity, finite-KL/FI, finite-log-mgf, boundary, smoothness, conditional-law, or stitched-interval hypothesis is added to a paper theorem as a hidden assumption.
4. No replacement of derivative -> LSI -> DV -> Gronwall, the correction-field specialization, or the paper EM/frozen-delta path.

lowerPacket : List String (explicit)

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

Ordered data items

1. Target exactly SALD.generalMovingTargetDiscreteDerivativeCandidateContract / SALD.generalMovingTargetDiscreteDerivativeObligation / sald.general_moving_target_discrete.kl_derivative.
2. First lower sub-slice remains appendix.tex:1354-1387: after the compiled Measure.map endpoint-law handoff, expose the common probability space, hat rho_s and tilde pi_s density/absolute-continuity, regular conditional drift bar b_{k,s}, weak conditional Fokker-Planck equation, KL differentiation under the integral, and integration-by-parts side conditions.
3. Use SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation only as endpoint-law bookkeeping and SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff only as sigma-weighted divergence algebra; do not classify either as the Brownian construction, regular conditional drift, density/absolute-continuity, weak Fokker-Planck, or KL derivative proof.
4. If the EM conditional-FP backend is blocked, sharpen the source-cited interface by naming the exact common-space, absolute-continuity, finite-KL/FI, measurability, endpoint, and conditional-law hypotheses rather than changing theorem statements.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. SALD.cycle54MainSkeletonAnalyticInterfaceObligation is listed by all six theorem contracts while they remain contractOnly.
2. SALD.saldDependenciesForLabel for the first proof-DAG labels includes the cycle-54 ledger, obligation, and DAG pane.
3. The conversion window and proof-obligation ledger contain the cycle-54 upper analytic-interface check and the lower packet over appendix.tex:1354-1387.
4. Gronwall, DV, LSI/KL/FI, continuous derivative, EM conditional-FP, and theorem statements are not promoted beyond their current statuses.
5. 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

1. SALD.cycle44MainSkeletonAnalyticInterfaceLedger
2. SALD.cycle49MainSkeletonAnalyticReadinessLedger
3. SALD.cycle50ForwardKlSkeletonObligation
4. SALD.cycle51DiscreteForwardKlSkeletonObligation
5. SALD.cycle52GuidedGeneralSkeletonObligation
6. SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation
7. SALD.saldGronwallEndpointCalculusContract
8. dvVariationalFormulaInterface saldDvVariationSource
9. SALD.saldLsiKlFiDensityTestContract
10. SALD.forwardKlDerivativeSideConditionContract
11. SALD.generalMovingTargetDerivativeCandidateContract
12. SALD.discreteForwardKlEmInterpolationSideConditionContract
13. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
14. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
15. SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff
16. SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation
17. sald.general_moving_target_discrete.kl_derivative

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

def cycle54MainSkeletonAnalyticInterfaceLedger :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteDerivativeSource
  objective := "Cycle 54 upper: re-run the main skeleton sprint-1 analytic interface ledger after cycles 50-53, check the five slow source-cited interfaces against all six theorem skeletons, and keep the next lower packet on the discrete general EM conditional-law/Fokker-Planck and KL-derivative backend."
  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 interface: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, the cycle-36/41 assembly wrappers, and theorem-specific Gronwall side-condition contracts expose closed-interval differentiability semantics, FTC/order integration, coefficient interval-integrability, endpoint evaluation, and exponent rewrites; lem:gronwall remains ProofStatus.obligation.",
    "DV interface: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific velocity/residual finite-log-mgf witness contracts expose same-space probability measures, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, alpha-range and positive-alpha scaling; the Boucheron variational equality remains ProofStatus.sourceCited.",
    "LSI/KL/FI interface: SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, and the cycle-43 density/entropy plus integral Fisher-chain helpers expose rho << pi, Radon-Nikodym density, zero-set convention, admissible sqrt-density test or approximation, entropy identity, finite KL/FI, and Fisher chain rule; probability.lsi_to_kl_fi remains ProofStatus.obligation.",
    "Continuous forward-KL/general Fokker-Planck/KL derivative interface: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and the cycle-50/52 scalar handoffs expose mass conservation, KL differentiation under the integral, SALD/general Fokker-Planck equations, target transport, integration by parts, LSI handoff, and inverse-schedule calculus; the analytic derivative backends remain ProofStatus.obligation.",
    "Euler-Maruyama interpolation Fokker-Planck interface: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, SALD.generalMovingTargetDiscreteEmEndpointLawPairOfNamedInterpolation, SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation, and SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff expose endpoint laws, named-law pushforward bookkeeping, regular conditional drift, density/absolute-continuity, weak conditional Fokker-Planck, Laplacian split, stitched intervals, and common-space assumptions; only endpoint-law congruence and the sigma-weighted divergence regrouping are formalized."
  ]
  theoremRoute := [
    "1. thm:forward-KL consumes the continuous KL derivative, LSI/KL/FI, DV velocity witness, endpoint schedule, and Gronwall side-condition interfaces from appendix.tex:168-252 and main_body.tex:238-247.",
    "2. thm:forward-KL-discrete consumes the EM endpoint/conditional-FP backend, frozen-defect estimate, LSI, DV velocity witness, stitched Gronwall, and accumulated-error bridge from appendix.tex:260-592 and main_body.tex:299-323.",
    "3. prop:guided_path_residual consumes only the normalizer derivative, guided-path differentiation, divergence cancellation, and mean-zero residual interfaces from appendix.tex:619-704; it remains the upstream input to the unified specialization.",
    "4. thm:general-moving-target-SALD consumes the continuous general derivative, residual Young/LSI, residual DV, sigma-weighted Gronwall, endpoint/exponent side conditions, and pure-contraction obligations from appendix.tex:724-949.",
    "5. thm:unified-forward-KL remains the paper specialization of thm:general-moving-target-SALD using prop:guided_path_residual and eq:poisson-eq, with no direct alternate KL proof.",
    "6. thm:general-moving-target-SALD-discrete consumes the general EM endpoint/conditional-FP backend, frozen-delta lemma, discrete KL derivative/LSI, residual DV, constant-schedule time change, and Gronwall stitching from appendix.tex:1313-1603."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: preserve main_body.tex, appendix.tex, and iteration_complexity.tex as the only source files; sald_version_2.tex remains excluded.",
    "Do not change theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, or proof routes.",
    "All unproved analytic backends stay obligation or sourceCited; only already compiled local scalar algebra and endpoint-law congruence helpers may be marked formalized.",
    "The next lower packet must improve a theorem-consumed backend interface, not start broad SLT/SDE backfill or a detached scalar lemma."
  ]
  nonGoals := [
    "No source-index rebaseline beyond the acceptance command.",
    "No imported SLT theorem is marked formalized for DV, LSI, concentration, disintegration, or one-step EM analysis.",
    "No endpoint, density, absolute-continuity, finite-KL/FI, finite-log-mgf, boundary, smoothness, conditional-law, or stitched-interval hypothesis is added to a paper theorem as a hidden assumption.",
    "No replacement of derivative -> LSI -> DV -> Gronwall, the correction-field specialization, or the paper EM/frozen-delta path."
  ]
  lowerPacket := [
    "Target exactly SALD.generalMovingTargetDiscreteDerivativeCandidateContract / SALD.generalMovingTargetDiscreteDerivativeObligation / sald.general_moving_target_discrete.kl_derivative.",
    "First lower sub-slice remains appendix.tex:1354-1387: after the compiled Measure.map endpoint-law handoff, expose the common probability space, hat rho_s and tilde pi_s density/absolute-continuity, regular conditional drift bar b_{k,s}, weak conditional Fokker-Planck equation, KL differentiation under the integral, and integration-by-parts side conditions.",
    "Use SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation only as endpoint-law bookkeeping and SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff only as sigma-weighted divergence algebra; do not classify either as the Brownian construction, regular conditional drift, density/absolute-continuity, weak Fokker-Planck, or KL derivative proof.",
    "If the EM conditional-FP backend is blocked, sharpen the source-cited interface by naming the exact common-space, absolute-continuity, finite-KL/FI, measurability, endpoint, and conditional-law hypotheses rather than changing theorem statements."
  ]
  reviewerChecklist := [
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation is listed by all six theorem contracts while they remain contractOnly.",
    "SALD.saldDependenciesForLabel for the first proof-DAG labels includes the cycle-54 ledger, obligation, and DAG pane.",
    "The conversion window and proof-obligation ledger contain the cycle-54 upper analytic-interface check and the lower packet over appendix.tex:1354-1387.",
    "Gronwall, DV, LSI/KL/FI, continuous derivative, EM conditional-FP, and theorem statements are not promoted beyond their current statuses.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle44MainSkeletonAnalyticInterfaceLedger",
    "SALD.cycle49MainSkeletonAnalyticReadinessLedger",
    "SALD.cycle50ForwardKlSkeletonObligation",
    "SALD.cycle51DiscreteForwardKlSkeletonObligation",
    "SALD.cycle52GuidedGeneralSkeletonObligation",
    "SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation",
    "SALD.saldGronwallEndpointCalculusContract",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
    "SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff",
    "SALD.cycle54GeneralMovingTargetDiscreteEmFpLowerObligation",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  status := ProofStatus.obligation

/-- Cycle-54 upper obligation for the repeated analytic-interface ledger. -/