Samplinglib
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AutoSamplingTheory.SALD.cycle67GuidedGeneralSkeletonUpperPacket

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 cycle67GuidedGeneralSkeletonUpperPacket : 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 67 upper: after the accepted cycle-66 discrete forward-KL route, wire prop:guided_path_residual and thm:general-moving-target-SALD through the already named guided residual, continuous derivative, LSI/KL/FI, residual DV, and sigma-weighted Gronwall interfaces over appendix.tex:619-951, preserving source statements and exposing the residual-to-Gronwall 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. prop:guided_path_residual
  2. eq:guided_path_residual
  3. eq:logZ_derivative
  4. thm:general-moving-target-SALD
  5. eq:general_moving_target_SALD
  6. eq:general_moving_target_KL_bound
  7. eq:general_moving_target_pure_contraction
  8. eq:general_KL_derivative_0
  9. eq:general_moving_target_FP
  10. eq:general_KL_derivative_1
  11. eq:general_KL_derivative_2
  12. eq:general_KL_derivative_3
  13. proof:thm:unified-forward-KL
  14. lem:gronwall
  15. lem:dv_variation
  16. eq:LSI-KL-FI
  17. 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 appendix.tex:619-951 exactly; sald_version_2.tex remains out of scope.
  2. Global phase judgment: cycle 66 passed reviewer/build and does not need recovery; Phase 1 is not stable enough for cited-theory backfill until this guided/general theorem route is rechecked; the selected lower packet is the residual-to-Gronwall bridge from appendix.tex:765-945.
  3. Five-backend check 1, Gronwall: consume SALD.saldGronwallEndpointCalculusContract, SALD.generalMovingTargetGronwallInstantiationContract, SALD.generalMovingTargetGronwallSideConditionContract, sald.general_moving_target.gronwall_application, and sald.general_moving_target.gronwall_side_conditions only as obligation-level endpoint/FTC/coefficient interfaces.
  4. Five-backend check 2, DV: consume dvVariationalFormulaInterface saldDvVariationSource, SALD.generalMovingTargetDvFiniteLogMgfWitnessContract, SALD.generalMovingTargetDvPositiveAlphaScalingContract, and sald.general_moving_target.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-57/62 scalar handoffs as local SDE/measure-analysis obligations.
  7. Five-backend check 5, EM interpolation: keep SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, and sald.general_moving_target_discrete.em_interpolation_fp visible only as downstream discrete interfaces.
nonGoals : List String (explicit)

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

Ordered data items

  1. Do not restate prop:guided_path_residual, thm:general-moving-target-SALD, or thm:unified-forward-KL.
  2. Do not prove or promote Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL differentiation, guided normalizer calculus, pure contraction, or EM interpolation.
  3. Do not add hidden smoothness, density, boundary, endpoint, finite-log-mgf, finite-KL/FI, coefficient-regularity, sigma-positivity, or schedule hypotheses to the paper theorem statements.
  4. Do not introduce Girsanov, Pinsker, Talagrand, path-space, PI, or direct VA-SALD proof routes.
  5. Do not start systematic SLT or SDE backfill in this upper packet; local SLT material remains reference-only.
lowerPacket : List String (explicit)

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

Ordered data items

  1. Middle should synchronize SALD.cycle67GuidedGeneralSkeletonUpperPacket, SALD.cycle67GuidedGeneralSkeletonObligation, and SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation into the conversion window, proof-obligation ledger, and SLT audit.
  2. Target exactly SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation / sald.general_moving_target.cycle67_residual_to_gronwall_bridge.
  3. First lower sub-slice: verify appendix.tex:765-884 is consumed in order by sald.general_moving_target.kl_derivative, the residual split/scaled-residual handoffs, SALD.saldLsiKlFiDensityTestContract, and the source schedule/sigma side-condition obligations.
  4. Second lower sub-slice: verify appendix.tex:885-907 is consumed by the residual DV finite-log-mgf and positive-alpha interfaces with Z=alpha*||m_t||^2.
  5. Third lower sub-slice: verify appendix.tex:908-945 is consumed by the sigma-weighted Gronwall instantiation, endpoint/exponent side-condition obligations, and pure-contraction zero-residual interface.
  6. 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.guidedResidualContract and SALD.generalVaSaldContract list SALD.cycle67GuidedGeneralSkeletonObligation and SALD.cycle67GuidedGeneralSkeletonMiddleObligation while remaining contractOnly.
  2. SALD.generalVaSaldContract lists SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation while thm:general-moving-target-SALD remains contractOnly.
  3. SALD.generalVaSaldProofDag contains ASTIS.SALD.guided_general.cycle67_guided_residual_route, ASTIS.SALD.guided_general.cycle67_general_moving_target_route, ASTIS.SALD.guided_general.cycle67_middle_route_audit, and ASTIS.SALD.guided_general.cycle67_lower_packet.residual_to_gronwall_bridge.
  4. SALD.saldDependenciesForLabel for prop:guided_path_residual and thm:general-moving-target-SALD includes the cycle-67 packet, upper and middle obligations, bridge, and DAG nodes.
  5. The five slow analytic interfaces remain source-cited or obligation-level; no theorem statement, source constant, source label, or external reuse 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 cycle67GuidedGeneralSkeletonUpperPacket : GeneralVaSaldUpperPacket where
  objective := "Cycle 67 upper: after the accepted cycle-66 discrete forward-KL route, wire prop:guided_path_residual and thm:general-moving-target-SALD through the already named guided residual, continuous derivative, LSI/KL/FI, residual DV, and sigma-weighted Gronwall interfaces over appendix.tex:619-951, preserving source statements and exposing the residual-to-Gronwall bridge as the single lower packet."
  sourceLabels := [
    "prop:guided_path_residual",
    "eq:guided_path_residual",
    "eq:logZ_derivative",
    "thm:general-moving-target-SALD",
    "eq:general_moving_target_SALD",
    "eq:general_moving_target_KL_bound",
    "eq:general_moving_target_pure_contraction",
    "eq:general_KL_derivative_0",
    "eq:general_moving_target_FP",
    "eq:general_KL_derivative_1",
    "eq:general_KL_derivative_2",
    "eq:general_KL_derivative_3",
    "proof:thm:unified-forward-KL",
    "lem:gronwall",
    "lem:dv_variation",
    "eq:LSI-KL-FI",
    "def:alpha-complexity"
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: use appendix.tex:619-951 exactly; sald_version_2.tex remains out of scope.",
    "Global phase judgment: cycle 66 passed reviewer/build and does not need recovery; Phase 1 is not stable enough for cited-theory backfill until this guided/general theorem route is rechecked; the selected lower packet is the residual-to-Gronwall bridge from appendix.tex:765-945.",
    "Five-backend check 1, Gronwall: consume SALD.saldGronwallEndpointCalculusContract, SALD.generalMovingTargetGronwallInstantiationContract, SALD.generalMovingTargetGronwallSideConditionContract, sald.general_moving_target.gronwall_application, and sald.general_moving_target.gronwall_side_conditions only as obligation-level endpoint/FTC/coefficient interfaces.",
    "Five-backend check 2, DV: consume dvVariationalFormulaInterface saldDvVariationSource, SALD.generalMovingTargetDvFiniteLogMgfWitnessContract, SALD.generalMovingTargetDvPositiveAlphaScalingContract, and sald.general_moving_target.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-57/62 scalar handoffs as local SDE/measure-analysis obligations.",
    "Five-backend check 5, EM interpolation: keep SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, and sald.general_moving_target_discrete.em_interpolation_fp visible only as downstream discrete interfaces."
  ]
  nonGoals := [
    "Do not restate prop:guided_path_residual, thm:general-moving-target-SALD, or thm:unified-forward-KL.",
    "Do not prove or promote Gronwall, DV, LSI/KL/FI, Fokker-Planck/KL differentiation, guided normalizer calculus, pure contraction, or EM interpolation.",
    "Do not add hidden smoothness, density, boundary, endpoint, finite-log-mgf, finite-KL/FI, coefficient-regularity, sigma-positivity, or schedule hypotheses to the paper theorem statements.",
    "Do not introduce Girsanov, Pinsker, Talagrand, path-space, PI, or direct VA-SALD proof routes.",
    "Do not start systematic SLT or SDE backfill in this upper packet; local SLT material remains reference-only."
  ]
  lowerPacket := [
    "Middle should synchronize SALD.cycle67GuidedGeneralSkeletonUpperPacket, SALD.cycle67GuidedGeneralSkeletonObligation, and SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation into the conversion window, proof-obligation ledger, and SLT audit.",
    "Target exactly SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation / sald.general_moving_target.cycle67_residual_to_gronwall_bridge.",
    "First lower sub-slice: verify appendix.tex:765-884 is consumed in order by sald.general_moving_target.kl_derivative, the residual split/scaled-residual handoffs, SALD.saldLsiKlFiDensityTestContract, and the source schedule/sigma side-condition obligations.",
    "Second lower sub-slice: verify appendix.tex:885-907 is consumed by the residual DV finite-log-mgf and positive-alpha interfaces with Z=alpha*||m_t||^2.",
    "Third lower sub-slice: verify appendix.tex:908-945 is consumed by the sigma-weighted Gronwall instantiation, endpoint/exponent side-condition obligations, and pure-contraction zero-residual interface.",
    "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.guidedResidualContract and SALD.generalVaSaldContract list SALD.cycle67GuidedGeneralSkeletonObligation and SALD.cycle67GuidedGeneralSkeletonMiddleObligation while remaining contractOnly.",
    "SALD.generalVaSaldContract lists SALD.cycle67GuidedGeneralResidualGronwallBridgeObligation while thm:general-moving-target-SALD remains contractOnly.",
    "SALD.generalVaSaldProofDag contains ASTIS.SALD.guided_general.cycle67_guided_residual_route, ASTIS.SALD.guided_general.cycle67_general_moving_target_route, ASTIS.SALD.guided_general.cycle67_middle_route_audit, and ASTIS.SALD.guided_general.cycle67_lower_packet.residual_to_gronwall_bridge.",
    "SALD.saldDependenciesForLabel for prop:guided_path_residual and thm:general-moving-target-SALD includes the cycle-67 packet, upper and middle obligations, bridge, and DAG nodes.",
    "The five slow analytic interfaces remain source-cited or obligation-level; no theorem statement, source constant, source label, or external reuse status changes.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  status := ProofStatus.obligation

/-- Cycle-67 upper obligation for the guided residual and continuous general
moving-target theorem route. -/

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