AutoSamplingTheory.SALD.cycle59MainSkeletonAnalyticMiddleContract

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 cycle59MainSkeletonAnalyticMiddleContract :
    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 middle: audit the upper analytic-interface ledger against the source proof order, verify that all six theorem skeletons consume the five slow interfaces explicitly, and keep the lower packet exactly on 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. appendix.tex:47-79
2. main_body.tex:202-215
3. appendix.tex:168-252
4. appendix.tex:260-592
5. appendix.tex:619-951
6. main_body.tex:359-395
7. appendix.tex:1313-1603
8. appendix.tex:1573-1600

analyticInterfaces : List String (explicit)

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

Ordered data items

1. Gronwall: theorem consumers use SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, theorem-specific side-condition contracts, and cycle-36/41/56/58 pointwise wrappers. Endpoint-safe differentiability, FTC/order integration, stitched endpoint laws, coefficient regularity, and final display matching remain obligations.
2. Donsker-Varadhan: theorem consumers use dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific finite-log-mgf witnesses. Common space, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, alpha monotonicity, and positive-alpha scaling remain source-cited or obligations.
3. LSI/KL/FI: theorem consumers use SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, probability.lsi_to_kl_fi, and the cycle-43 density/entropy/Fisher-chain helpers. Zero-set handling, admissible sqrt-density test or approximation, finite KL/FI, and vector Fisher chain rule remain obligations.
4. Continuous Fokker-Planck/KL derivative: thm:forward-KL and thm:general-moving-target-SALD consume SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and the cycle-50/52/55/57 scalar handoffs. Density, boundary, mass conservation, target transport, integration by parts, and schedule calculus remain obligations.
5. Euler-Maruyama interpolation Fokker-Planck: discrete theorem consumers use SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, the cycle-48/53 endpoint-law handoffs, SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff, and the cycle-58 pointwise Gronwall-input wrapper. Conditional drift, density/absolute-continuity, weak FP, KL differentiation, and integration by parts remain obligations.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. thm:forward-KL is still derivative -> LSI -> DV velocity -> endpoint schedule -> Gronwall, with source display main_body.tex:238-247 and proof appendix.tex:168-252.
2. 2. thm:forward-KL-discrete is still EM endpoint/conditional-FP -> frozen defect -> LSI -> DV velocity -> stitched Gronwall -> accumulated error, with source display main_body.tex:299-323 and proof appendix.tex:260-592.
3. 3. prop:guided_path_residual is still normalizer derivative -> guided-density differentiation -> divergence cancellation -> mean-zero residual over appendix.tex:619-704.
4. 4. thm:general-moving-target-SALD is still continuous general derivative split -> residual LSI/DV -> sigma-weighted Gronwall -> pure contraction over appendix.tex:724-951.
5. 5. thm:unified-forward-KL is still the paper specialization of thm:general-moving-target-SALD via prop:guided_path_residual, eq:poisson-eq, c_t=u_t, and m_t=w_t.
6. 6. thm:general-moving-target-SALD-discrete is still general EM endpoint/conditional-FP -> frozen delta -> discrete KL derivative/LSI -> residual DV -> constant schedule -> cycle-58 pointwise Gronwall input -> final 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. Do not change theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, or proof order.
3. Keep every unproved analytic backend below formalized status; local compiled scalar or endpoint-law helpers stay dependencies only.
4. The next lower packet must be a theorem-consumed backend over appendix.tex:1573-1600, not broad SLT/SDE backfill.

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 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 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. Target exactly SALD.generalMovingTargetDiscreteGronwallSideConditionContract / SALD.generalMovingTargetDiscreteGronwallSideConditionObligation / sald.general_moving_target_discrete.gronwall_side_conditions.
2. First sub-slice: appendix.tex:1573-1583 endpoint stitching for K(t), including K(0)=KL(rho_0||pi_0), K(T)=KL(rho_K^eta||pi_T), interval compatibility, and constant inverse-schedule admissibility.
3. Second sub-slice: appendix.tex:1584-1597 coefficient regularity and exact a(t), b(t) display matching, reusing SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged, SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput, and the constant-schedule coefficient rewrite scalars only as local inputs.
4. Third sub-slice: appendix.tex:1600 endpoint-safe Gronwall application and final theorem-display matching against appendix.tex:1316-1347.
5. If proof-producing work blocks, sharpen the endpoint, common-space, absolute-continuity, finite-KL/FI, measurability, schedule, coefficient, and stitched-interval interfaces 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.cycle59MainSkeletonAnalyticMiddleObligation is listed by all six theorem contracts while they remain contractOnly.
2. SALD.cycle59MainSkeletonAnalyticInterfaceDag contains ASTIS.SALD.cycle59.middle_interface_audit between the upper route rewire and lower packet.
3. SALD.saldDependenciesForLabel includes the cycle-59 middle contract, middle obligation, and middle DAG node through cycle59MainSkeletonDependencyNames.
4. The conversion window, proof-obligation ledger, and SLT reuse audit contain the cycle-59 middle audit and keep the lower packet on appendix.tex:1573-1600.
5. Gronwall, DV, LSI/KL/FI, continuous derivative, EM conditional-FP, theorem contracts, and SLT reuse statuses are not promoted.
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.cycle59MainSkeletonAnalyticInterfaceLedger
2. SALD.cycle59MainSkeletonAnalyticInterfaceObligation
3. SALD.cycle58UnifiedDiscreteGeneralMiddleObligation
4. SALD.cycle56DiscreteForwardKlGronwallLowerObligation
5. SALD.cycle55ForwardKlSkeletonMiddleObligation
6. SALD.cycle57GuidedGeneralSkeletonMiddleObligation
7. SALD.saldGronwallEndpointCalculusContract
8. dvVariationalFormulaInterface saldDvVariationSource
9. SALD.saldLsiKlFiDensityTestContract
10. SALD.forwardKlDerivativeSideConditionContract
11. SALD.generalMovingTargetDerivativeCandidateContract
12. SALD.discreteForwardKlEmInterpolationSideConditionContract
13. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
14. SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged
15. SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput
16. SALD.generalMovingTargetDiscreteGronwallEndpointRewriteScalar
17. SALD.generalMovingTargetDiscreteGronwallSideConditionContract
18. 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

def cycle59MainSkeletonAnalyticMiddleContract :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteGronwallSideConditionSource
  objective := "Cycle 59 middle: audit the upper analytic-interface ledger against the source proof order, verify that all six theorem skeletons consume the five slow interfaces explicitly, and keep the lower packet exactly on sald.general_moving_target_discrete.gronwall_side_conditions over appendix.tex:1573-1600."
  sourceLabels := [
    "appendix.tex:47-79",
    "main_body.tex:202-215",
    "appendix.tex:168-252",
    "appendix.tex:260-592",
    "appendix.tex:619-951",
    "main_body.tex:359-395",
    "appendix.tex:1313-1603",
    "appendix.tex:1573-1600"
  ]
  analyticInterfaces := [
    "Gronwall: theorem consumers use SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, theorem-specific side-condition contracts, and cycle-36/41/56/58 pointwise wrappers. Endpoint-safe differentiability, FTC/order integration, stitched endpoint laws, coefficient regularity, and final display matching remain obligations.",
    "Donsker-Varadhan: theorem consumers use dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, and theorem-specific finite-log-mgf witnesses. Common space, absolute continuity, finite KL/log-likelihood, selected-test measurability, finite log-mgf, alpha monotonicity, and positive-alpha scaling remain source-cited or obligations.",
    "LSI/KL/FI: theorem consumers use SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, probability.lsi_to_kl_fi, and the cycle-43 density/entropy/Fisher-chain helpers. Zero-set handling, admissible sqrt-density test or approximation, finite KL/FI, and vector Fisher chain rule remain obligations.",
    "Continuous Fokker-Planck/KL derivative: thm:forward-KL and thm:general-moving-target-SALD consume SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and the cycle-50/52/55/57 scalar handoffs. Density, boundary, mass conservation, target transport, integration by parts, and schedule calculus remain obligations.",
    "Euler-Maruyama interpolation Fokker-Planck: discrete theorem consumers use SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, the cycle-48/53 endpoint-law handoffs, SALD.generalMovingTargetDiscreteConditionalFpSigmaLaplacianSplitHandoff, and the cycle-58 pointwise Gronwall-input wrapper. Conditional drift, density/absolute-continuity, weak FP, KL differentiation, and integration by parts remain obligations."
  ]
  theoremRoute := [
    "1. thm:forward-KL is still derivative -> LSI -> DV velocity -> endpoint schedule -> Gronwall, with source display main_body.tex:238-247 and proof appendix.tex:168-252.",
    "2. thm:forward-KL-discrete is still EM endpoint/conditional-FP -> frozen defect -> LSI -> DV velocity -> stitched Gronwall -> accumulated error, with source display main_body.tex:299-323 and proof appendix.tex:260-592.",
    "3. prop:guided_path_residual is still normalizer derivative -> guided-density differentiation -> divergence cancellation -> mean-zero residual over appendix.tex:619-704.",
    "4. thm:general-moving-target-SALD is still continuous general derivative split -> residual LSI/DV -> sigma-weighted Gronwall -> pure contraction over appendix.tex:724-951.",
    "5. thm:unified-forward-KL is still the paper specialization of thm:general-moving-target-SALD via prop:guided_path_residual, eq:poisson-eq, c_t=u_t, and m_t=w_t.",
    "6. thm:general-moving-target-SALD-discrete is still general EM endpoint/conditional-FP -> frozen delta -> discrete KL derivative/LSI -> residual DV -> constant schedule -> cycle-58 pointwise Gronwall input -> final display stitching."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: use only main_body.tex, appendix.tex, and iteration_complexity.tex; sald_version_2.tex remains excluded.",
    "Do not change theorem statements, constants, alpha ranges, sigma factors, endpoint laws, source labels, or proof order.",
    "Keep every unproved analytic backend below formalized status; local compiled scalar or endpoint-law helpers stay dependencies only.",
    "The next lower packet must be a theorem-consumed backend over appendix.tex:1573-1600, not broad SLT/SDE backfill."
  ]
  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 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 theorem.",
    "No alternate proof route replaces derivative -> LSI -> DV -> Gronwall, the correction-field specialization, or the paper EM/frozen-delta route."
  ]
  lowerPacket := [
    "Target exactly SALD.generalMovingTargetDiscreteGronwallSideConditionContract / SALD.generalMovingTargetDiscreteGronwallSideConditionObligation / sald.general_moving_target_discrete.gronwall_side_conditions.",
    "First sub-slice: appendix.tex:1573-1583 endpoint stitching for K(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 sub-slice: appendix.tex:1584-1597 coefficient regularity and exact a(t), b(t) display matching, reusing SALD.generalMovingTargetDiscretePointwiseGronwallInputOfPostDvTimeChanged, SALD.generalMovingTargetDiscreteGronwallNamedCoefficientInput, and the constant-schedule coefficient rewrite scalars only as local inputs.",
    "Third sub-slice: appendix.tex:1600 endpoint-safe Gronwall application and final theorem-display matching against appendix.tex:1316-1347.",
    "If proof-producing work blocks, sharpen the endpoint, common-space, absolute-continuity, finite-KL/FI, measurability, schedule, coefficient, and stitched-interval interfaces rather than changing theorem statements."
  ]
  reviewerChecklist := [
    "SALD.cycle59MainSkeletonAnalyticMiddleObligation is listed by all six theorem contracts while they remain contractOnly.",
    "SALD.cycle59MainSkeletonAnalyticInterfaceDag contains ASTIS.SALD.cycle59.middle_interface_audit between the upper route rewire and lower packet.",
    "SALD.saldDependenciesForLabel includes the cycle-59 middle contract, middle obligation, and middle DAG node through cycle59MainSkeletonDependencyNames.",
    "The conversion window, proof-obligation ledger, and SLT reuse audit contain the cycle-59 middle audit and keep the lower packet on appendix.tex:1573-1600.",
    "Gronwall, DV, LSI/KL/FI, continuous derivative, EM conditional-FP, theorem contracts, and SLT reuse statuses are not promoted.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle59MainSkeletonAnalyticInterfaceLedger",
    "SALD.cycle59MainSkeletonAnalyticInterfaceObligation",
    "SALD.cycle58UnifiedDiscreteGeneralMiddleObligation",
    "SALD.cycle56DiscreteForwardKlGronwallLowerObligation",
    "SALD.cycle55ForwardKlSkeletonMiddleObligation",
    "SALD.cycle57GuidedGeneralSkeletonMiddleObligation",
    "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 middle obligation tying the analytic-interface audit to the six
theorem consumers and the selected lower Gronwall/display packet. -/