Samplinglib
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AutoSamplingTheory.SALD.cycle59MainSkeletonAnalyticInterfaceLedger

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 cycle59MainSkeletonAnalyticInterfaceLedger :
    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.saldGeneralMovingTargetDiscreteGronwallSideConditionSource — 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 59 upper: after the accepted cycle-58 reviewer/build gate, re-check the five source-cited analytic interfaces and wire the post-cycle-58 theorem route back into all six SALD theorem consumers. Phase 1 is stable enough for one narrow cited-theory/SDE backfill, but not for broad reusable API work; the single lower packet remains sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600.
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. proof:thm:general-moving-target-SALD-discrete:gronwall-side-conditions
  9. thm:forward-KL
  10. thm:forward-KL-discrete
  11. prop:guided_path_residual
  12. thm:general-moving-target-SALD
  13. thm:unified-forward-KL
  14. 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. Global phase judgment: cycle 58 passed reviewer and build, so no failed previous cycle must be recovered before cycle 59 work.
  2. Global phase judgment: Phase 1 theorem-skeleton translation is stable enough to begin exactly one narrow cited-theory/SDE backend after this ledger, but broad measure-theory, SLT, or reusable API reorganization remains deferred.
  3. Global phase judgment: the lower packet that best reduces remaining proof risk is sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600, because it is the last theorem-display step after the EM derivative/DV handoff.
  4. Gronwall: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, theorem-specific Gronwall instantiation contracts, and the cycle-36/41 wrappers expose endpoint-safe differentiability/FTC, interval integrability, endpoint evaluation, exponent algebra, stitched regularity, and coefficient/display side conditions; lem:gronwall remains ProofStatus.obligation.
  5. Donsker-Varadhan: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific finite-log-mgf witnesses expose common-space probability measures, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, alpha monotonicity, and positive-alpha scaling; the Boucheron variational equality remains ProofStatus.sourceCited.
  6. LSI/KL/FI: SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, and the cycle-43 density/entropy/Fisher-chain helpers expose rho << pi, Radon-Nikodym density, zero-density convention, admissible sqrt-density test or approximation, entropy identity, finite KL/FI, and Fisher chain rule; probability.lsi_to_kl_fi remains ProofStatus.obligation.
  7. Continuous Fokker-Planck/KL derivative: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and the cycle-50/52/57 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; analytic derivative backends remain ProofStatus.obligation.
  8. Euler-Maruyama interpolation Fokker-Planck: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, the cycle-48/53 endpoint-law handoffs, SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff, and the cycle-58 pointwise Gronwall-input wrapper expose endpoint laws, named-law pushforward bookkeeping, regular conditional drift, density/absolute-continuity, weak conditional FP, Laplacian split, stitched intervals, time change, and common-space assumptions without promoting the EM backend.
theoremRoute : List String (explicit)

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

Ordered data items

  1. 1. thm:forward-KL remains wired through continuous KL derivative/Fokker-Planck, eq:LSI-KL-FI, DV velocity witness, endpoint schedule, and Gronwall side conditions.
  2. 2. thm:forward-KL-discrete remains wired through EM endpoint/conditional-FP, frozen defect, LSI, DV velocity, stitched Gronwall, and accumulated-error interfaces, including the recovered cycle-56 Gronwall input wrapper.
  3. 3. prop:guided_path_residual remains wired through normalizer differentiation, guided-density differentiation, divergence cancellation, and mean-zero residual obligations.
  4. 4. thm:general-moving-target-SALD remains wired through the continuous general derivative split, residual LSI/DV, sigma-weighted Gronwall, endpoint/exponent side conditions, and pure-contraction obligation.
  5. 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, and c_t=u_t, m_t=w_t.
  6. 6. thm:general-moving-target-SALD-discrete remains wired through general EM endpoint/conditional-FP, frozen-delta, discrete KL derivative/LSI, residual DV, constant-schedule time change, the cycle-58 pointwise Gronwall input, and final Gronwall/display stitching.
modeDiscipline : List String (explicit)

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

Ordered data items

  1. faithfulPaper Phase 1: use only main_body.tex, appendix.tex, and iteration_complexity.tex; sald_version_2.tex remains excluded.
  2. Keep source theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, and proof order fixed.
  3. Keep every unproved analytic backend below formalized status; already compiled scalar or endpoint-law helpers are dependencies only.
  4. Systematic cited-theory backfill may begin only one backend at a time after this ledger and must remain tied to a theorem route.
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 unless a reviewer reports a source-anchor defect.
  2. No broad SLT import, concentration port, disintegration port, or reusable teaching API reorganization in this upper packet.
  3. 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 paper theorem.
  4. 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

  1. Middle should synchronize this cycle-59 analytic-interface ledger with conversion-windows/ASTIS-SALD-001.md and proof-obligations/ASTIS-SALD-001.md, then keep the theorem route in the order forward-KL, discrete forward-KL, guided residual, general moving-target, unified forward-KL, discrete general moving-target.
  2. Lower should target exactly SALD.generalMovingTargetDiscreteGronwallSideConditionContract / SALD.generalMovingTargetDiscreteGronwallSideConditionObligation / sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600.
  3. First lower sub-slice: endpoint stitching for K(t)=KL(hat rho_{s(t)}||pi_t), including K(0)=KL(rho_0||pi_0), K(T)=KL(rho_K^eta||pi_T), interval compatibility, and constant inverse-schedule admissibility.
  4. Second lower sub-slice: coefficient regularity and exact display matching for a(t) and b(t), reusing SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged, SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput, and the constant-schedule coefficient rewrite scalars only as local inputs.
  5. If proof-producing work is blocked, sharpen the source-cited interface by naming endpoint, common-space, absolute-continuity, finite-KL/FI, measurability, schedule, and coefficient hypotheses rather than modifying theorem statements.
reviewerChecklist : List String (explicit)

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

Ordered data items

  1. SALD.cycle59MainSkeletonAnalyticInterfaceObligation is listed by all six theorem contracts while they remain contractOnly.
  2. All four theorem proof DAGs include SALD.cycle59MainSkeletonAnalyticInterfaceDag, and saldDependenciesForLabel includes the cycle-59 dependency names for the five slow interfaces and six theorem labels.
  3. The conversion window and proof-obligation ledger contain the cycle-59 global phase judgment, five-interface check, theorem route, lower packet, and reviewer checklist.
  4. Gronwall, DV, LSI/KL/FI, continuous derivative, EM conditional-FP, theorem contracts, and SLT reuse statuses 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.cycle44MainSkeletonAnalyticInterfaceObligation
  2. SALD.cycle54MainSkeletonAnalyticInterfaceObligation
  3. SALD.cycle54MainSkeletonAnalyticMiddleObligation
  4. SALD.cycle55ForwardKlSkeletonMiddleObligation
  5. SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation
  6. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
  7. SALD.cycle57GuidedGeneralSkeletonMiddleObligation
  8. SALD.cycle58UnifiedDiscreteGeneralMiddleObligation
  9. SALD.saldGronwallEndpointCalculusContract
  10. dvVariationalFormulaInterface saldDvVariationSource
  11. SALD.saldLsiKlFiDensityTestContract
  12. SALD.forwardKlDerivativeSideConditionContract
  13. SALD.generalMovingTargetDerivativeCandidateContract
  14. SALD.discreteForwardKlEmInterpolationSideConditionContract
  15. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
  16. SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged
  17. SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput
  18. SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar
  19. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
  20. sald.general_moving_target_discrete.gronwall_side_conditions
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 cycle59MainSkeletonAnalyticInterfaceLedger :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
  objective := "Cycle 59 upper: after the accepted cycle-58 reviewer/build gate, re-check the five source-cited analytic interfaces and wire the post-cycle-58 theorem route back into all six SALD theorem consumers. Phase 1 is stable enough for one narrow cited-theory/SDE backfill, but not for broad reusable API work; the single lower packet remains sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600."
  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",
    "proof:thm:general-moving-target-SALD-discrete:gronwall-side-conditions",
    "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 := [
    "Global phase judgment: cycle 58 passed reviewer and build, so no failed previous cycle must be recovered before cycle 59 work.",
    "Global phase judgment: Phase 1 theorem-skeleton translation is stable enough to begin exactly one narrow cited-theory/SDE backend after this ledger, but broad measure-theory, SLT, or reusable API reorganization remains deferred.",
    "Global phase judgment: the lower packet that best reduces remaining proof risk is sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600, because it is the last theorem-display step after the EM derivative/DV handoff.",
    "Gronwall: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, theorem-specific Gronwall instantiation contracts, and the cycle-36/41 wrappers expose endpoint-safe differentiability/FTC, interval integrability, endpoint evaluation, exponent algebra, stitched regularity, and coefficient/display side conditions; lem:gronwall remains ProofStatus.obligation.",
    "Donsker-Varadhan: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific finite-log-mgf witnesses expose common-space probability measures, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, alpha monotonicity, and positive-alpha scaling; the Boucheron variational equality remains ProofStatus.sourceCited.",
    "LSI/KL/FI: SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, and the cycle-43 density/entropy/Fisher-chain helpers expose rho << pi, Radon-Nikodym density, zero-density 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 Fokker-Planck/KL derivative: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and the cycle-50/52/57 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; analytic derivative backends remain ProofStatus.obligation.",
    "Euler-Maruyama interpolation Fokker-Planck: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, the cycle-48/53 endpoint-law handoffs, SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff, and the cycle-58 pointwise Gronwall-input wrapper expose endpoint laws, named-law pushforward bookkeeping, regular conditional drift, density/absolute-continuity, weak conditional FP, Laplacian split, stitched intervals, time change, and common-space assumptions without promoting the EM backend."
  ]
  theoremRoute := [
    "1. thm:forward-KL remains wired through continuous KL derivative/Fokker-Planck, eq:LSI-KL-FI, DV velocity witness, endpoint schedule, and Gronwall side conditions.",
    "2. thm:forward-KL-discrete remains wired through EM endpoint/conditional-FP, frozen defect, LSI, DV velocity, stitched Gronwall, and accumulated-error interfaces, including the recovered cycle-56 Gronwall input wrapper.",
    "3. prop:guided_path_residual remains wired through normalizer differentiation, guided-density differentiation, divergence cancellation, and mean-zero residual obligations.",
    "4. thm:general-moving-target-SALD remains wired through the continuous general derivative split, residual LSI/DV, sigma-weighted Gronwall, endpoint/exponent side conditions, and pure-contraction obligation.",
    "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, and c_t=u_t, m_t=w_t.",
    "6. thm:general-moving-target-SALD-discrete remains wired through general EM endpoint/conditional-FP, frozen-delta, discrete KL derivative/LSI, residual DV, constant-schedule time change, the cycle-58 pointwise Gronwall input, and final Gronwall/display stitching."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: use only main_body.tex, appendix.tex, and iteration_complexity.tex; sald_version_2.tex remains excluded.",
    "Keep source theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, and proof order fixed.",
    "Keep every unproved analytic backend below formalized status; already compiled scalar or endpoint-law helpers are dependencies only.",
    "Systematic cited-theory backfill may begin only one backend at a time after this ledger and must remain tied to a theorem route."
  ]
  nonGoals := [
    "No source-index rebaseline beyond the acceptance command unless a reviewer reports a source-anchor defect.",
    "No broad SLT import, concentration port, disintegration port, or reusable teaching API reorganization in this upper packet.",
    "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 paper theorem.",
    "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-59 analytic-interface ledger with conversion-windows/ASTIS-SALD-001.md and proof-obligations/ASTIS-SALD-001.md, then keep the theorem route in the order forward-KL, discrete forward-KL, guided residual, general moving-target, unified forward-KL, discrete general moving-target.",
    "Lower should target exactly SALD.generalMovingTargetDiscreteGronwallSideConditionContract / SALD.generalMovingTargetDiscreteGronwallSideConditionObligation / sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600.",
    "First lower sub-slice: endpoint stitching for K(t)=KL(hat rho_{s(t)}||pi_t), including K(0)=KL(rho_0||pi_0), K(T)=KL(rho_K^eta||pi_T), interval compatibility, and constant inverse-schedule admissibility.",
    "Second lower sub-slice: coefficient regularity and exact display matching for a(t) and b(t), reusing SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged, SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput, and the constant-schedule coefficient rewrite scalars only as local inputs.",
    "If proof-producing work is blocked, sharpen the source-cited interface by naming endpoint, common-space, absolute-continuity, finite-KL/FI, measurability, schedule, and coefficient hypotheses rather than modifying theorem statements."
  ]
  reviewerChecklist := [
    "SALD.cycle59MainSkeletonAnalyticInterfaceObligation is listed by all six theorem contracts while they remain contractOnly.",
    "All four theorem proof DAGs include SALD.cycle59MainSkeletonAnalyticInterfaceDag, and saldDependenciesForLabel includes the cycle-59 dependency names for the five slow interfaces and six theorem labels.",
    "The conversion window and proof-obligation ledger contain the cycle-59 global phase judgment, five-interface check, theorem route, lower packet, and reviewer checklist.",
    "Gronwall, DV, LSI/KL/FI, continuous derivative, EM conditional-FP, theorem contracts, and SLT reuse statuses 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.cycle44MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle54MainSkeletonAnalyticMiddleObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleObligation",
    "SALD.cycle56DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
    "SALD.cycle57GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle58UnifiedDiscreteGeneralMiddleObligation",
    "SALD.saldGronwallEndpointCalculusContract",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged",
    "SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput",
    "SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar",
    "SALD.generalMovingTargetDiscreteGronwallSideConditionContract",
    "sald.general_moving_target_discrete.gronwall_side_conditions"
  ]
  status := ProofStatus.obligation

/-- Cycle-59 upper obligation for the analytic-interface recheck. -/

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