Samplinglib
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AutoSamplingTheory.SALD.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket

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 cycle68UnifiedDiscreteGeneralSkeletonUpperPacket :
    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 68 upper: after the accepted cycle-67 guided/general route, wire thm:unified-forward-KL and thm:general-moving-target-SALD-discrete through the continuous general skeletons and the explicit source-cited interfaces, preserving the main-body and appendix theorem statements while selecting the discrete general EM/derivative/DV/Gronwall theorem bridge as the single lower packet.
sourceLabels : List String (explicit)

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

Ordered data items

  1. thm:unified-forward-KL
  2. eq:ito_forward_KL_bound_calibrated
  3. proof:thm:unified-forward-KL
  4. prop:guided_path_residual
  5. eq:poisson-eq
  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. eq:general_discrete_delta_def
  11. lem:frozen_delta_cross_lip
  12. eq:general_KL_derivative_0_discrete
  13. eq:general_KL_derivative_8_discrete
  14. eq:general_moving_target_KL_bound_discrete
  15. lem:gronwall
  16. lem:dv_variation
  17. eq:LSI-KL-FI
  18. def:alpha-complexity
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 exactly; sald_version_2.tex remains out of scope.
  2. Global phase judgment: cycle 67 passed reviewer/build and does not need recovery; Phase 1 theorem-skeleton translation is stable enough to finish the unified/discrete-general route before any cited-theory backfill; the selected lower packet is the discrete general theorem bridge from EM endpoint/conditional-law through derivative, DV, and Gronwall/display.
  3. Five-backend check 1, Gronwall: consume SALD.saldGronwallEndpointCalculusContract, SALD.generalMovingTargetGronwallSideConditionContract, SALD.generalMovingTargetDiscreteGronwallInstantiationContract, SALD.generalMovingTargetDiscreteGronwallSideConditionContract, and the cycle-59/67 wrappers only as obligation-level endpoint/FTC/coefficient/display interfaces.
  4. Five-backend check 2, DV: consume dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, SALD.generalMovingTargetDvFiniteLogMgfWitnessContract, SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract, sald.general_moving_target.dv_m_energy, and sald.general_moving_target_discrete.dv_m_energy with common-space, absolute-continuity, finite-KL, finite-log-mgf, measurability, and positive-alpha side conditions explicit.
  5. Five-backend check 3, LSI/KL/FI: consume SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, and probability.lsi_to_kl_fi while preserving density, zero-set, admissible sqrt-density test, entropy identity, finite KL/FI, and Fisher chain-rule obligations.
  6. Five-backend check 4, continuous derivative: consume SALD.generalMovingTargetDerivativeCandidateContract, SALD.generalMovingTargetDerivativeObligation, sald.general_moving_target.kl_derivative, and cycle-67 residual-to-Gronwall handoffs as local SDE/measure-analysis obligations used by thm:unified-forward-KL through specialization.
  7. Five-backend check 5, EM interpolation: consume SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, cycle-63 endpoint-law helpers, cycle-64 conditional-drift interface, and sald.general_moving_target_discrete.em_interpolation_fp as downstream discrete obligations, not as formalized theorem backends.
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 add hidden density, boundary, endpoint, finite-log-mgf, finite-KL/FI, common-space, conditional-law, coefficient-regularity, sigma-positivity, or schedule assumptions to the paper theorem statements.
  3. Do not prove or promote Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL differentiation, EM conditional Fokker-Planck, frozen-delta, residual DV, or final Gronwall/display matching.
  4. Do not replace the appendix specialization of thm:unified-forward-KL with a direct VA-SALD proof route.
  5. Do not start broad SLT/SDE library import; local SLT material may guide only a later narrow backend after this route is synchronized.
lowerPacket : List String (explicit)

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

Ordered data items

  1. Middle should synchronize SALD.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket, SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation, and SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation into the conversion window, proof-obligation ledger, and SLT audit.
  2. Target exactly SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation / sald.unified_discrete_general.cycle68_discrete_general_bridge.
  3. First lower sub-slice: verify main_body.tex:359-395 and appendix.tex:949-951 are consumed by prop:guided_path_residual, eq:poisson-eq, SALD.unifiedForwardKlSpecializationContract, sald.unified_forward_kl.transport_velocity_bridge, sald.unified_forward_kl.specialization, and the cycle-67 continuous general route.
  4. Second lower sub-slice: verify appendix.tex:1313-1387 is consumed by the fixed discrete statement, endpoint law/common-space helpers, conditional drift, weak EM Fokker-Planck, and KL derivative side-condition interfaces.
  5. Third lower sub-slice: verify appendix.tex:1455-1588 is consumed by frozen-delta, Young/LSI, residual DV with Z=alpha*||m_t||^2, constant-schedule time change, and the pointwise Gronwall input.
  6. Fourth lower sub-slice: verify appendix.tex:1316-1347 and 1588-1603 are consumed by SALD.generalMovingTargetDiscreteGronwallSideConditionContract and display-matching obligations.
  7. If any analytic step is too large, sharpen only the named source-cited or obligation interface; do not change theorem statements, constants, labels, or proof route.
reviewerChecklist : List String (explicit)

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

Ordered data items

  1. SALD.unifiedForwardKlContract lists SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation while remaining contractOnly.
  2. SALD.generalVaSaldDiscreteContract lists SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation and SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation while remaining contractOnly.
  3. SALD.generalVaSaldProofDag and SALD.generalVaSaldDiscreteProofDag contain SALD.cycle68UnifiedDiscreteGeneralDag after the cycle-67 and cycle-63 route data.
  4. SALD.saldDependenciesForLabel for thm:unified-forward-KL and thm:general-moving-target-SALD-discrete includes SALD.cycle68UnifiedDiscreteGeneralDependencyNames.
  5. The five slow analytic interfaces remain source-cited or obligation-level; no theorem statement, source constant, source label, external reuse status, or theorem status changes.
  6. 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 cycle68UnifiedDiscreteGeneralSkeletonUpperPacket :
    GeneralVaSaldUpperPacket where
  objective := "Cycle 68 upper: after the accepted cycle-67 guided/general route, wire thm:unified-forward-KL and thm:general-moving-target-SALD-discrete through the continuous general skeletons and the explicit source-cited interfaces, preserving the main-body and appendix theorem statements while selecting the discrete general EM/derivative/DV/Gronwall theorem bridge as the single lower packet."
  sourceLabels := [
    "thm:unified-forward-KL",
    "eq:ito_forward_KL_bound_calibrated",
    "proof:thm:unified-forward-KL",
    "prop:guided_path_residual",
    "eq:poisson-eq",
    "thm:general-moving-target-SALD",
    "thm:general-moving-target-SALD-discrete",
    "eq:SALD_general_EM",
    "eq:general_moving_target_SALD_frozen_interp",
    "eq:general_discrete_delta_def",
    "lem:frozen_delta_cross_lip",
    "eq:general_KL_derivative_0_discrete",
    "eq:general_KL_derivative_8_discrete",
    "eq:general_moving_target_KL_bound_discrete",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: use main_body.tex:359-395, appendix.tex:949-951, and appendix.tex:1313-1603 exactly; sald_version_2.tex remains out of scope.",
    "Global phase judgment: cycle 67 passed reviewer/build and does not need recovery; Phase 1 theorem-skeleton translation is stable enough to finish the unified/discrete-general route before any cited-theory backfill; the selected lower packet is the discrete general theorem bridge from EM endpoint/conditional-law through derivative, DV, and Gronwall/display.",
    "Five-backend check 1, Gronwall: consume SALD.saldGronwallEndpointCalculusContract, SALD.generalMovingTargetGronwallSideConditionContract, SALD.generalMovingTargetDiscreteGronwallInstantiationContract, SALD.generalMovingTargetDiscreteGronwallSideConditionContract, and the cycle-59/67 wrappers only as obligation-level endpoint/FTC/coefficient/display interfaces.",
    "Five-backend check 2, DV: consume dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, SALD.generalMovingTargetDvFiniteLogMgfWitnessContract, SALD.generalMovingTargetDiscreteDvFiniteLogMgfWitnessContract, sald.general_moving_target.dv_m_energy, and sald.general_moving_target_discrete.dv_m_energy with common-space, absolute-continuity, finite-KL, finite-log-mgf, measurability, and positive-alpha side conditions explicit.",
    "Five-backend check 3, LSI/KL/FI: consume SALD.saldLsiKlFiDensityTestContract, SALD.lsiKlFiDensityTestObligation, and probability.lsi_to_kl_fi while preserving density, zero-set, admissible sqrt-density test, entropy identity, finite KL/FI, and Fisher chain-rule obligations.",
    "Five-backend check 4, continuous derivative: consume SALD.generalMovingTargetDerivativeCandidateContract, SALD.generalMovingTargetDerivativeObligation, sald.general_moving_target.kl_derivative, and cycle-67 residual-to-Gronwall handoffs as local SDE/measure-analysis obligations used by thm:unified-forward-KL through specialization.",
    "Five-backend check 5, EM interpolation: consume SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, cycle-63 endpoint-law helpers, cycle-64 conditional-drift interface, and sald.general_moving_target_discrete.em_interpolation_fp as downstream discrete obligations, not as formalized theorem backends."
  ]
  nonGoals := [
    "Do not restate thm:unified-forward-KL, thm:general-moving-target-SALD, or thm:general-moving-target-SALD-discrete.",
    "Do not add hidden density, boundary, endpoint, finite-log-mgf, finite-KL/FI, common-space, conditional-law, coefficient-regularity, sigma-positivity, or schedule assumptions to the paper theorem statements.",
    "Do not prove or promote Gronwall, DV, LSI/KL/FI, continuous Fokker-Planck/KL differentiation, EM conditional Fokker-Planck, frozen-delta, residual DV, or final Gronwall/display matching.",
    "Do not replace the appendix specialization of thm:unified-forward-KL with a direct VA-SALD proof route.",
    "Do not start broad SLT/SDE library import; local SLT material may guide only a later narrow backend after this route is synchronized."
  ]
  lowerPacket := [
    "Middle should synchronize SALD.cycle68UnifiedDiscreteGeneralSkeletonUpperPacket, SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation, and SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation into the conversion window, proof-obligation ledger, and SLT audit.",
    "Target exactly SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation / sald.unified_discrete_general.cycle68_discrete_general_bridge.",
    "First lower sub-slice: verify main_body.tex:359-395 and appendix.tex:949-951 are consumed by prop:guided_path_residual, eq:poisson-eq, SALD.unifiedForwardKlSpecializationContract, sald.unified_forward_kl.transport_velocity_bridge, sald.unified_forward_kl.specialization, and the cycle-67 continuous general route.",
    "Second lower sub-slice: verify appendix.tex:1313-1387 is consumed by the fixed discrete statement, endpoint law/common-space helpers, conditional drift, weak EM Fokker-Planck, and KL derivative side-condition interfaces.",
    "Third lower sub-slice: verify appendix.tex:1455-1588 is consumed by frozen-delta, Young/LSI, residual DV with Z=alpha*||m_t||^2, constant-schedule time change, and the pointwise Gronwall input.",
    "Fourth lower sub-slice: verify appendix.tex:1316-1347 and 1588-1603 are consumed by SALD.generalMovingTargetDiscreteGronwallSideConditionContract and display-matching obligations.",
    "If any analytic step is too large, sharpen only the named source-cited or obligation interface; do not change theorem statements, constants, labels, or proof route."
  ]
  reviewerChecklist := [
    "SALD.unifiedForwardKlContract lists SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation while remaining contractOnly.",
    "SALD.generalVaSaldDiscreteContract lists SALD.cycle68UnifiedDiscreteGeneralSkeletonObligation and SALD.cycle68UnifiedDiscreteGeneralDiscreteBridgeObligation while remaining contractOnly.",
    "SALD.generalVaSaldProofDag and SALD.generalVaSaldDiscreteProofDag contain SALD.cycle68UnifiedDiscreteGeneralDag after the cycle-67 and cycle-63 route data.",
    "SALD.saldDependenciesForLabel for thm:unified-forward-KL and thm:general-moving-target-SALD-discrete includes SALD.cycle68UnifiedDiscreteGeneralDependencyNames.",
    "The five slow analytic interfaces remain source-cited or obligation-level; no theorem statement, source constant, source label, external reuse status, or theorem status changes.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  status := ProofStatus.obligation

/-- Cycle-68 upper obligation for routing the unified and discrete general
theorems through the accepted continuous/general skeletons and explicit slow
interfaces. -/

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