Samplinglib
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AutoSamplingTheory.SALD.cycle53UnifiedDiscreteGeneralUpperPacket

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.SALD.GeneralVaSaldUpperPacket. 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 cycle53UnifiedDiscreteGeneralUpperPacket : GeneralVaSaldUpperPacket

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.

objective : String (explicit)

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

Cycle 53 upper: close main skeleton sprint 5 by wiring thm:unified-forward-KL through the cycle-52 continuous general theorem route and wiring thm:general-moving-target-SALD-discrete through the explicit source-cited EM, derivative, LSI, residual-DV, and Gronwall interfaces; after that route check, add one narrow Measure.map endpoint-law backfill for the discrete general EM interpolation.
sourceLabels : List String (explicit)

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

Ordered data items

  1. thm:unified-forward-KL
  2. proof:thm:unified-forward-KL
  3. eq:SALD_Ito
  4. eq:poisson-eq
  5. prop:guided_path_residual
  6. thm:general-moving-target-SALD
  7. thm:general-moving-target-SALD-discrete
  8. eq:SALD_general_EM
  9. eq:general_moving_target_SALD_frozen_interp
  10. proof:thm:general-moving-target-SALD-discrete:derivative
  11. proof:thm:general-moving-target-SALD-discrete:residual-dv
  12. proof:thm:general-moving-target-SALD-discrete:gronwall
  13. lem:gronwall
  14. lem:dv_variation
  15. eq:LSI-KL-FI
modeDiscipline : List String (explicit)

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

Ordered data items

  1. faithfulPaper Phase 1: use main_body.tex:359-395, appendix.tex:949-951, and appendix.tex:1313-1603 only; sald_version_2.tex remains excluded.
  2. Five-backend check 1, Gronwall: use SALD.saldGronwallEndpointCalculusContract and the general/discrete Gronwall side-condition obligations for endpoint-safe differentiability, FTC, coefficient regularity, stitching, and display matching.
  3. Five-backend check 2, DV: use dvVariationalFormulaInterface saldDvVariationSource plus residual finite-log-mgf/common-space witnesses for continuous and EM-interpolated residual fields; the Boucheron equality remains sourceCited.
  4. Five-backend check 3, LSI/KL/FI: use SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, and probability.lsi_to_kl_fi for density, zero-set, admissible sqrt test, entropy, and Fisher-chain assumptions.
  5. Five-backend check 4, continuous derivative: consume SALD.generalMovingTargetDerivativeCandidateContract, SALD.generalMovingTargetDerivativeObligation, and the cycle-52 scalar derivative/DV handoff without promoting the Fokker-Planck or integration-by-parts backend.
  6. Five-backend check 5, EM interpolation: consume SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, and the endpoint-law handoffs while keeping conditional drift, density/absolute-continuity, and weak Fokker-Planck as obligations.
  7. Only after the theorem route is wired, the measure-theory backfill is limited to AutoSamplingTheory.lawMapEqOfAEEq and SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation.
nonGoals : List String (explicit)

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

Ordered data items

  1. Do not restate thm:unified-forward-KL, thm:general-moving-target-SALD, or thm:general-moving-target-SALD-discrete.
  2. Do not introduce a direct unified VA-SALD KL proof; the source route remains c_t=u_t specialization of the continuous general theorem.
  3. Do not prove or promote Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL derivative, regular conditional drift, density/absolute-continuity, conditional Fokker-Planck, frozen-delta, or theorem-level statements.
  4. Do not import or mark any SLT theorem as formalized; local SLT pushforward-law patterns are reference-only for this narrow Measure.map congruence backfill.
  5. Do not change the doubled residual coefficient, Gamma/Delta terms, alpha ranges, sigma_eta factors, endpoint labels, or source theorem displays.
lowerPacket : List String (explicit)

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

Ordered data items

  1. Middle should synchronize the conversion window, proof-obligation ledger, and SLT audit for SALD.cycle53UnifiedDiscreteGeneralUpperPacket / SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation.
  2. Preferred lower target remains SALD.generalMovingTargetDiscreteDerivativeCandidateContract / SALD.generalMovingTargetDiscreteDerivativeObligation / sald.general_moving_target_discrete.kl_derivative over appendix.tex:1354-1387.
  3. First lower sub-slice after the compiled endpoint backfill: connect the Measure.map endpoint-law equality to the named hat rho_s/rho_k^eta representation, then expose common-space, density/absolute-continuity, regular conditional drift, and weak conditional Fokker-Planck interfaces.
  4. Alternative lower target only if discrete KL derivative is blocked: sald.unified_forward_kl.transport_velocity_bridge, preserving the residual/correction signs from main_body.tex:359-368.
  5. If any analytic backend is too large, refine its named source-cited interface rather than adding hidden assumptions to the theorem contract.
reviewerChecklist : List String (explicit)

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

Ordered data items

  1. SALD.unifiedForwardKlContract and SALD.generalVaSaldDiscreteContract list SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation while remaining contractOnly.
  2. SALD.generalVaSaldProofDag and SALD.generalVaSaldDiscreteProofDag include ASTIS.SALD.unified_discrete_general.cycle53_upper_route.
  3. SALD.saldDependenciesForLabel for thm:unified-forward-KL and thm:general-moving-target-SALD-discrete includes the cycle-53 packet, obligation, DAG route, and the compiled Measure.map endpoint-law backfill.
  4. AutoSamplingTheory.lawMapEqOfAEEq and SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation are the only new formalized backfill lemmas; all large analytic backends remain obligation or source-cited.
  5. python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass.
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 cycle53UnifiedDiscreteGeneralUpperPacket : GeneralVaSaldUpperPacket where
  objective := "Cycle 53 upper: close main skeleton sprint 5 by wiring thm:unified-forward-KL through the cycle-52 continuous general theorem route and wiring thm:general-moving-target-SALD-discrete through the explicit source-cited EM, derivative, LSI, residual-DV, and Gronwall interfaces; after that route check, add one narrow Measure.map endpoint-law backfill for the discrete general EM interpolation."
  sourceLabels := [
    "thm:unified-forward-KL",
    "proof:thm:unified-forward-KL",
    "eq:SALD_Ito",
    "eq:poisson-eq",
    "prop:guided_path_residual",
    "thm:general-moving-target-SALD",
    "thm:general-moving-target-SALD-discrete",
    "eq:SALD_general_EM",
    "eq:general_moving_target_SALD_frozen_interp",
    "proof:thm:general-moving-target-SALD-discrete:derivative",
    "proof:thm:general-moving-target-SALD-discrete:residual-dv",
    "proof:thm:general-moving-target-SALD-discrete:gronwall",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI"
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: use main_body.tex:359-395, appendix.tex:949-951, and appendix.tex:1313-1603 only; sald_version_2.tex remains excluded.",
    "Five-backend check 1, Gronwall: use SALD.saldGronwallEndpointCalculusContract and the general/discrete Gronwall side-condition obligations for endpoint-safe differentiability, FTC, coefficient regularity, stitching, and display matching.",
    "Five-backend check 2, DV: use dvVariationalFormulaInterface saldDvVariationSource plus residual finite-log-mgf/common-space witnesses for continuous and EM-interpolated residual fields; the Boucheron equality remains sourceCited.",
    "Five-backend check 3, LSI/KL/FI: use SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, and probability.lsi_to_kl_fi for density, zero-set, admissible sqrt test, entropy, and Fisher-chain assumptions.",
    "Five-backend check 4, continuous derivative: consume SALD.generalMovingTargetDerivativeCandidateContract, SALD.generalMovingTargetDerivativeObligation, and the cycle-52 scalar derivative/DV handoff without promoting the Fokker-Planck or integration-by-parts backend.",
    "Five-backend check 5, EM interpolation: consume SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, and the endpoint-law handoffs while keeping conditional drift, density/absolute-continuity, and weak Fokker-Planck as obligations.",
    "Only after the theorem route is wired, the measure-theory backfill is limited to AutoSamplingTheory.lawMapEqOfAEEq and SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation."
  ]
  nonGoals := [
    "Do not restate thm:unified-forward-KL, thm:general-moving-target-SALD, or thm:general-moving-target-SALD-discrete.",
    "Do not introduce a direct unified VA-SALD KL proof; the source route remains c_t=u_t specialization of the continuous general theorem.",
    "Do not prove or promote Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL derivative, regular conditional drift, density/absolute-continuity, conditional Fokker-Planck, frozen-delta, or theorem-level statements.",
    "Do not import or mark any SLT theorem as formalized; local SLT pushforward-law patterns are reference-only for this narrow Measure.map congruence backfill.",
    "Do not change the doubled residual coefficient, Gamma/Delta terms, alpha ranges, sigma_eta factors, endpoint labels, or source theorem displays."
  ]
  lowerPacket := [
    "Middle should synchronize the conversion window, proof-obligation ledger, and SLT audit for SALD.cycle53UnifiedDiscreteGeneralUpperPacket / SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation.",
    "Preferred lower target remains SALD.generalMovingTargetDiscreteDerivativeCandidateContract / SALD.generalMovingTargetDiscreteDerivativeObligation / sald.general_moving_target_discrete.kl_derivative over appendix.tex:1354-1387.",
    "First lower sub-slice after the compiled endpoint backfill: connect the Measure.map endpoint-law equality to the named hat rho_s/rho_k^eta representation, then expose common-space, density/absolute-continuity, regular conditional drift, and weak conditional Fokker-Planck interfaces.",
    "Alternative lower target only if discrete KL derivative is blocked: sald.unified_forward_kl.transport_velocity_bridge, preserving the residual/correction signs from main_body.tex:359-368.",
    "If any analytic backend is too large, refine its named source-cited interface rather than adding hidden assumptions to the theorem contract."
  ]
  reviewerChecklist := [
    "SALD.unifiedForwardKlContract and SALD.generalVaSaldDiscreteContract list SALD.cycle53UnifiedDiscreteGeneralSkeletonObligation while remaining contractOnly.",
    "SALD.generalVaSaldProofDag and SALD.generalVaSaldDiscreteProofDag include ASTIS.SALD.unified_discrete_general.cycle53_upper_route.",
    "SALD.saldDependenciesForLabel for thm:unified-forward-KL and thm:general-moving-target-SALD-discrete includes the cycle-53 packet, obligation, DAG route, and the compiled Measure.map endpoint-law backfill.",
    "AutoSamplingTheory.lawMapEqOfAEEq and SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation are the only new formalized backfill lemmas; all large analytic backends remain obligation or source-cited.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  status := ProofStatus.obligation

/-- Cycle-53 obligation tying the final unified/discrete general theorem route
to explicit source-cited interfaces and the narrow Measure.map endpoint
backfill. -/

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