AutoSamplingTheory.SALD.cycle69MainSkeletonAnalyticInterfaceLedger

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 cycle69MainSkeletonAnalyticInterfaceLedger :
    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.saldGeneralMovingTargetDiscreteSource — 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 69 upper: cycle 68 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for a post-route analytic-interface ledger and only one narrow backend backfill, not broad cited-theory or reusable API work; the single lower packet that best reduces proof risk is the shared Euler-Maruyama interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387, because it supports both discrete theorem skeletons and remains the largest common measure/SDE dependency.

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:em-conditional-fp
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: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, and theorem-specific Gronwall side-condition contracts expose endpoint-safe differentiability or right-derivative/FTC assumptions, interval integrability, endpoint evaluation, coefficient regularity, and exponent/display rewrites; lem:gronwall remains ProofStatus.obligation.
2. Donsker-Varadhan: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific finite-log-mgf witness contracts expose common probability space, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, positive-alpha scaling, and E_alpha rewriting; the cited variational equality remains ProofStatus.sourceCited.
3. LSI/KL/FI: SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, probability.lsi_to_kl_fi, and the cycle-33/38/43 helper rows expose Radon-Nikodym density, zero-set convention, admissible sqrt-density test or approximation, entropy identity, finite KL/FI, and the vector/integral Fisher chain rule; eq:LSI-KL-FI remains ProofStatus.obligation.
4. Continuous forward-KL Fokker-Planck/KL derivative: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and the cycle-60/65/67 scalar handoffs expose mass conservation, KL differentiation under the integral, Fokker-Planck substitution, integration by parts, target transport, residual Young/LSI, and inverse-schedule calculus; analytic derivative backends remain ProofStatus.obligation.
5. Euler-Maruyama interpolation Fokker-Planck: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, cycle-63 endpoint-law helpers, cycle-64 conditional-drift algebra, 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 interval regularity; this is the selected lower packet and remains ProofStatus.obligation.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. thm:forward-KL consumes continuous KL derivative/Fokker-Planck, LSI/KL/FI, DV velocity-energy, inverse-schedule calculus, and Gronwall endpoint/exponent display matching.
2. 2. thm:forward-KL-discrete consumes EM endpoint/conditional-FP, KL derivative with frozen defect and LSI, DV velocity, time-changed Gronwall, and accumulated-error display matching.
3. 3. prop:guided_path_residual consumes guided normalizer differentiation, quotient/product calculus, divergence cancellation, and centered residual mean-zero obligations.
4. 4. thm:general-moving-target-SALD consumes continuous general KL derivative, residual Young/LSI, residual DV, sigma-weighted Gronwall, endpoint/exponent side conditions, and pure-contraction specialization.
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, c_t=u_t, and m_t=w_t.
6. 6. thm:general-moving-target-SALD-discrete consumes general EM endpoint/conditional-FP, frozen-delta, KL derivative/LSI, residual DV, constant-schedule time change, 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 the original main_body.tex, appendix.tex, and iteration_complexity.tex; sald_version_2.tex remains excluded.
2. Keep theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, and source proof order fixed.
3. Every unproved slow analytic backend remains ProofStatus.obligation or ProofStatus.sourceCited; compiled scalar, endpoint-law, and display wrappers are local dependencies only.
4. A future lower run may backfill exactly one backend, the EM interpolation conditional-law/Fokker-Planck interface, but this upper ledger only sharpens the interface and 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 required acceptance command unless a reviewer reports a blocking source-anchor defect.
2. No broad SLT import, Gaussian concentration port, entropy-duality project, disintegration project, SDE library reorganization, or teaching API rewrite.
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 any source theorem statement.
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-69 analytic-interface ledger with conversion-windows/ASTIS-SALD-001.md and proof-obligations/ASTIS-SALD-001.md, preserving the six theorem-route order.
2. Lower should target exactly SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation / SALD.generalMovingTargetDiscreteDerivativeSideConditionContract / sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.
3. First sub-slice: expose the common probability space, endpoint laws for hat rho_s and tilde pi_s, density/absolute-continuity, finite KL, and mass-conservation hypotheses needed before differentiating KL.
4. Second sub-slice: sharpen the regular conditional law of X_k^eta given hat X_s=x and the measurable/integrable conditional drift bar b_{k,s}(x), reusing the cycle-64 conditional-drift linear-combination algebra only under supplied conditional-expectation linearity.
5. Third sub-slice: state the weak conditional Fokker-Planck equation with the exact source signs -div(hat rho_s bar b_{k,s}) and +(sigma_eta^2/2) Delta hat rho_s, leaving KL differentiation, LSI, DV, Gronwall, and theorem closure as separate obligations.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. SALD.cycle69MainSkeletonAnalyticInterfaceObligation is listed by all six theorem contracts while those contracts remain ProofStatus.contractOnly.
2. SALD.forwardKlProofDag, SALD.discreteForwardKlProofDag, SALD.generalVaSaldProofDag, and SALD.generalVaSaldDiscreteProofDag include SALD.cycle69MainSkeletonAnalyticInterfaceDag.
3. SALD.saldDependenciesForLabel includes cycle69MainSkeletonDependencyNames for the five slow interfaces and all six theorem-route labels.
4. The selected lower packet is the EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387, not a theorem-status promotion or broad SLT/SDE port.
5. 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.
6. 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.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation
2. SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation
3. SALD.cycle67GuidedGeneralSkeletonMiddleObligation
4. SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation
5. SALD.cycle65ForwardKlSkeletonMiddleObligation
6. SALD.cycle64MainSkeletonAnalyticInterfaceObligation
7. SALD.saldGronwallEndpointCalculusContract
8. dvVariationalFormulaInterface saldDvVariationSource
9. SALD.saldLsiKlFiDensityTestContract
10. SALD.forwardKlDerivativeSideConditionContract
11. SALD.generalMovingTargetDerivativeCandidateContract
12. SALD.discreteForwardKlEmInterpolationSideConditionContract
13. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
14. SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation
15. SALD.generalMovingTargetDiscreteConditionalDriftContract
16. sald.general_moving_target_discrete.em_interpolation_fp

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 cycle69MainSkeletonAnalyticInterfaceLedger :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteSource
  objective := "Cycle 69 upper: cycle 68 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for a post-route analytic-interface ledger and only one narrow backend backfill, not broad cited-theory or reusable API work; the single lower packet that best reduces proof risk is the shared Euler-Maruyama interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387, because it supports both discrete theorem skeletons and remains the largest common measure/SDE dependency."
  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:em-conditional-fp",
    "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 theorem-specific Gronwall side-condition contracts expose endpoint-safe differentiability or right-derivative/FTC assumptions, interval integrability, endpoint evaluation, coefficient regularity, and exponent/display rewrites; lem:gronwall remains ProofStatus.obligation.",
    "Donsker-Varadhan: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific finite-log-mgf witness contracts expose common probability space, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, positive-alpha scaling, and E_alpha rewriting; the cited variational equality remains ProofStatus.sourceCited.",
    "LSI/KL/FI: SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, probability.lsi_to_kl_fi, and the cycle-33/38/43 helper rows expose Radon-Nikodym density, zero-set convention, admissible sqrt-density test or approximation, entropy identity, finite KL/FI, and the vector/integral Fisher chain rule; eq:LSI-KL-FI remains ProofStatus.obligation.",
    "Continuous forward-KL Fokker-Planck/KL derivative: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and the cycle-60/65/67 scalar handoffs expose mass conservation, KL differentiation under the integral, Fokker-Planck substitution, integration by parts, target transport, residual Young/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 helpers, cycle-64 conditional-drift algebra, 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 interval regularity; this is the selected lower packet and remains ProofStatus.obligation."
  ]
  theoremRoute := [
    "1. thm:forward-KL consumes continuous KL derivative/Fokker-Planck, LSI/KL/FI, DV velocity-energy, inverse-schedule calculus, and Gronwall endpoint/exponent display matching.",
    "2. thm:forward-KL-discrete consumes EM endpoint/conditional-FP, KL derivative with frozen defect and LSI, DV velocity, time-changed Gronwall, and accumulated-error display matching.",
    "3. prop:guided_path_residual consumes guided normalizer differentiation, quotient/product calculus, divergence cancellation, and centered residual mean-zero obligations.",
    "4. thm:general-moving-target-SALD consumes continuous general KL derivative, 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 consumes general EM endpoint/conditional-FP, frozen-delta, KL derivative/LSI, residual DV, constant-schedule time change, and final Gronwall/display stitching."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: use only the original main_body.tex, appendix.tex, and iteration_complexity.tex; sald_version_2.tex remains excluded.",
    "Keep theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, and source proof order fixed.",
    "Every unproved slow analytic backend remains ProofStatus.obligation or ProofStatus.sourceCited; compiled scalar, endpoint-law, and display wrappers are local dependencies only.",
    "A future lower run may backfill exactly one backend, the EM interpolation conditional-law/Fokker-Planck interface, but this upper ledger only sharpens the interface and route."
  ]
  nonGoals := [
    "No source-index rebaseline beyond the required acceptance command unless a reviewer reports a blocking source-anchor defect.",
    "No broad SLT import, Gaussian concentration port, entropy-duality project, disintegration project, SDE library reorganization, 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 any 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-69 analytic-interface ledger with conversion-windows/ASTIS-SALD-001.md and proof-obligations/ASTIS-SALD-001.md, preserving the six theorem-route order.",
    "Lower should target exactly SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation / SALD.generalMovingTargetDiscreteDerivativeSideConditionContract / sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.",
    "First sub-slice: expose the common probability space, endpoint laws for hat rho_s and tilde pi_s, density/absolute-continuity, finite KL, and mass-conservation hypotheses needed before differentiating KL.",
    "Second sub-slice: sharpen the regular conditional law of X_k^eta given hat X_s=x and the measurable/integrable conditional drift bar b_{k,s}(x), reusing the cycle-64 conditional-drift linear-combination algebra only under supplied conditional-expectation linearity.",
    "Third sub-slice: state the weak conditional Fokker-Planck equation with the exact source signs -div(hat rho_s bar b_{k,s}) and +(sigma_eta^2/2) Delta hat rho_s, leaving KL differentiation, LSI, DV, Gronwall, and theorem closure as separate obligations."
  ]
  reviewerChecklist := [
    "SALD.cycle69MainSkeletonAnalyticInterfaceObligation is listed by all six theorem contracts while those contracts remain ProofStatus.contractOnly.",
    "SALD.forwardKlProofDag, SALD.discreteForwardKlProofDag, SALD.generalVaSaldProofDag, and SALD.generalVaSaldDiscreteProofDag include SALD.cycle69MainSkeletonAnalyticInterfaceDag.",
    "SALD.saldDependenciesForLabel includes cycle69MainSkeletonDependencyNames for the five slow interfaces and all six theorem-route labels.",
    "The selected lower packet is the EM interpolation conditional-law/Fokker-Planck backend over appendix.tex:1358-1387, not a 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.cycle68UnifiedDiscreteGeneralSkeletonMiddleObligation",
    "SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeLowerObligation",
    "SALD.cycle67GuidedGeneralSkeletonMiddleObligation",
    "SALD.cycle66DiscreteForwardKlSkeletonMiddleObligation",
    "SALD.cycle65ForwardKlSkeletonMiddleObligation",
    "SALD.cycle64MainSkeletonAnalyticInterfaceObligation",
    "SALD.saldGronwallEndpointCalculusContract",
    "dvVariationalFormulaInterface saldDvVariationSource",
    "SALD.saldLsiKlFiDensityTestContract",
    "SALD.forwardKlDerivativeSideConditionContract",
    "SALD.generalMovingTargetDerivativeCandidateContract",
    "SALD.discreteForwardKlEmInterpolationSideConditionContract",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  status := ProofStatus.obligation

/-- Cycle-69 upper obligation for the post-route analytic-interface ledger. -/