AutoSamplingTheory.SALD.cycle62GuidedGeneralSkeletonUpperPacket

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.

def cycle62GuidedGeneralSkeletonUpperPacket : 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 62 upper: cycle 61 passed reviewer/build and needs no recovery; Phase 1 is not stable enough for cited-theory backfill until prop:guided_path_residual and thm:general-moving-target-SALD are rechecked after the discrete route recovery; the single lower packet is a guided residual to general moving-target route audit over appendix.tex:619-951 that narrows proof search back to sald.general_moving_target.kl_derivative.

sourceLabels : List String (explicit)

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

Ordered data items

1. prop:guided_path_residual
2. proof:prop:guided_path_residual
3. thm:general-moving-target-SALD
4. eq:general_moving_target_SALD
5. eq:general_moving_target_FP
6. proof:thm:general-moving-target-SALD:derivative
7. proof:thm:general-moving-target-SALD:residual-dv
8. proof:thm:general-moving-target-SALD:dv-gronwall
9. proof:thm:general-moving-target-SALD:pure-contraction
10. proof:thm:unified-forward-KL
11. eq:LSI-KL-FI
12. lem:dv_variation
13. lem:gronwall
14. def:alpha-complexity

modeDiscipline : List String (explicit)

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

Ordered data items

1. Global phase judgment: cycle 61 did not fail and needs no recovery; it accepted the recovered thm:forward-KL-discrete route and accumulated-error bridge while keeping theorem and backend statuses below formalized.
2. Global phase judgment: Phase 1 theorem-skeleton translation is not yet stable enough for cited-theory backfill, because the guided residual and continuous general moving-target theorem route must be rechecked after the discrete recovery.
3. Global phase judgment: the lower packet that reduces the largest current proof risk is the appendix.tex:619-951 guided residual to general moving-target route audit, with lower proof search narrowed to sald.general_moving_target.kl_derivative once the audit is synchronized.
4. Five-backend check 1, Gronwall: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, and SALD.gronwallAnalyticObligation keep endpoint-safe differentiability, FTC/order integration, coefficient regularity, endpoint rewrites, exponent splitting, and residual-exponent side conditions explicit.
5. Five-backend check 2, DV: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, SALD.generalMovingTargetDvFiniteLogMgfWitnessContract, and SALD.generalMovingTargetDvPositiveAlphaScalingContract keep common-space, absolute-continuity, finite KL, finite log-mgf, measurability of alpha*||m_t||^2, and positive-alpha scaling explicit.
6. Five-backend check 3, LSI/KL/FI: SALD.saldLsiKlFiDensityTestContract and probability.lsi_to_kl_fi keep density, zero-set convention, admissible sqrt-density test, entropy identity, finite KL/FI, and Fisher chain-rule assumptions explicit.
7. Five-backend check 4, continuous Fokker-Planck/KL derivative: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and sald.general_moving_target.kl_derivative keep density/law regularity, mass conservation, integration by parts, target transport, sigma positivity, and inverse-schedule side conditions explicit.
8. Five-backend check 5, EM interpolation Fokker-Planck: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, and sald.general_moving_target_discrete.em_interpolation_fp expose endpoint laws, conditional drift, conditional-law density/absolute-continuity, weak Fokker-Planck, Laplacian split, and stitched-interval interfaces for downstream discrete reuse.
9. The theorem route check remains in paper order: forward-KL through cycle 60, discrete forward-KL through cycle 61, guided residual through the normalizer and identity obligations, general moving-target through derivative/LSI/DV/Gronwall/pure-contraction interfaces, unified forward-KL as the c_t<-u_t specialization, and discrete general moving-target through the existing EM/frozen-delta/LSI/DV/Gronwall interfaces.
10. FaithfulPaper Phase 1: use appendix.tex:619-951 and the original main_body.tex unified reference only; sald_version_2.tex remains excluded.

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, thm:unified-forward-KL, or any theorem display.
2. Do not add hidden density, endpoint, common-space, finite-log-mgf, sigma-positivity, schedule, or coefficient-regularity assumptions to the source theorem statements.
3. Do not promote guided residual calculus, Fokker-Planck/KL differentiation, LSI/KL/FI, DV, Gronwall, pure contraction, EM interpolation, or any theorem status above contractOnly/sourceCited/obligation.
4. Do not replace the source route by a direct VA-SALD proof, path-space comparison, Girsanov, Pinsker, Talagrand, PI, or SLT-based proof.
5. Do not begin systematic measure-theory or SDE backfill in this upper cycle; missing analytic facts must stay as source-cited interfaces or obligations.

lowerPacket : List String (explicit)

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

Ordered data items

1. Middle should synchronize this cycle-62 upper route with conversion-windows/ASTIS-SALD-001.md, proof-obligations/ASTIS-SALD-001.md, and the guided/general proof DAG before lower proof search.
2. Lower route audit target: appendix.tex:619-951, checking that every guided residual and general moving-target proof step maps to SALD.guidedResidualIdentityContract, SALD.generalMovingTargetDerivativeCandidateContract, SALD.saldLsiKlFiDensityTestContract, SALD.generalMovingTargetDvFiniteLogMgfWitnessContract, SALD.generalMovingTargetGronwallSideConditionContract, or a named obligation.
3. After the route audit is accepted, proof-producing lower work should target exactly SALD.generalMovingTargetDerivativeCandidateContract / SALD.generalMovingTargetDerivativeObligation / sald.general_moving_target.kl_derivative over appendix.tex:765-884.
4. First derivative sub-slice: appendix.tex:765-812, exposing law regularity, mass conservation, KL differentiation under the integral, the general moving-target Fokker-Planck equation, and integration-by-parts side conditions.
5. Second derivative sub-slice: appendix.tex:813-864, exposing target transport by v_t, rescaled transport of pi_{t(s)}, residual m_t=v_t-c_t, and Young with epsilon=2*dot t(s)/sigma_{t(s)}^2.
6. Third derivative sub-slice: appendix.tex:865-884, preserving the LSI handoff and s-to-t schedule/sigma side conditions without adding them to the theorem statement.
7. Leave guided normalizer differentiation, residual DV finite-log-mgf, Gronwall endpoint/exponent, pure contraction, unified specialization, and downstream EM interpolation as separate obligations unless exact compiled proofs are added.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. The cycle-62 route uses cycle 61 as the recovered discrete forward-KL prerequisite and does not reopen the cycle-56 failure.
2. SALD.guidedResidualContract and SALD.generalVaSaldContract list SALD.cycle62GuidedGeneralSkeletonObligation while remaining contractOnly.
3. SALD.generalVaSaldProofDag contains ASTIS.SALD.guided_general.cycle62_global_phase_judgment, cycle62_five_backend_check, cycle62_upper_route, and the selected lower-packet node.
4. SALD.saldDependenciesForLabel for prop:guided_path_residual and thm:general-moving-target-SALD includes the cycle-62 packet, obligation, and DAG nodes.
5. The five slow analytic interfaces remain source-cited or obligation-level; no source theorem statement, source constant, source label, SLT reuse status, or analytic backend 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

def cycle62GuidedGeneralSkeletonUpperPacket : GeneralVaSaldUpperPacket where
  objective := "Cycle 62 upper: cycle 61 passed reviewer/build and needs no recovery; Phase 1 is not stable enough for cited-theory backfill until prop:guided_path_residual and thm:general-moving-target-SALD are rechecked after the discrete route recovery; the single lower packet is a guided residual to general moving-target route audit over appendix.tex:619-951 that narrows proof search back to sald.general_moving_target.kl_derivative."
  sourceLabels := [
    "prop:guided_path_residual",
    "proof:prop:guided_path_residual",
    "thm:general-moving-target-SALD",
    "eq:general_moving_target_SALD",
    "eq:general_moving_target_FP",
    "proof:thm:general-moving-target-SALD:derivative",
    "proof:thm:general-moving-target-SALD:residual-dv",
    "proof:thm:general-moving-target-SALD:dv-gronwall",
    "proof:thm:general-moving-target-SALD:pure-contraction",
    "proof:thm:unified-forward-KL",
    "eq:LSI-KL-FI",
    "lem:dv_variation",
    "lem:gronwall",
    "def:alpha-complexity"
  ]
  modeDiscipline := [
    "Global phase judgment: cycle 61 did not fail and needs no recovery; it accepted the recovered thm:forward-KL-discrete route and accumulated-error bridge while keeping theorem and backend statuses below formalized.",
    "Global phase judgment: Phase 1 theorem-skeleton translation is not yet stable enough for cited-theory backfill, because the guided residual and continuous general moving-target theorem route must be rechecked after the discrete recovery.",
    "Global phase judgment: the lower packet that reduces the largest current proof risk is the appendix.tex:619-951 guided residual to general moving-target route audit, with lower proof search narrowed to sald.general_moving_target.kl_derivative once the audit is synchronized.",
    "Five-backend check 1, Gronwall: SALD.saldGronwallCandidateContract, SALD.saldGronwallEndpointCalculusContract, SALD.saldGronwallExponentRewriteContract, and SALD.gronwallAnalyticObligation keep endpoint-safe differentiability, FTC/order integration, coefficient regularity, endpoint rewrites, exponent splitting, and residual-exponent side conditions explicit.",
    "Five-backend check 2, DV: dvVariationalFormulaInterface saldDvVariationSource, SALD.saldDvFiniteLogMgfContract, SALD.generalMovingTargetDvFiniteLogMgfWitnessContract, and SALD.generalMovingTargetDvPositiveAlphaScalingContract keep common-space, absolute-continuity, finite KL, finite log-mgf, measurability of alpha*||m_t||^2, and positive-alpha scaling explicit.",
    "Five-backend check 3, LSI/KL/FI: SALD.saldLsiKlFiDensityTestContract and probability.lsi_to_kl_fi keep density, zero-set convention, admissible sqrt-density test, entropy identity, finite KL/FI, and Fisher chain-rule assumptions explicit.",
    "Five-backend check 4, continuous Fokker-Planck/KL derivative: SALD.forwardKlDerivativeCandidateContract, SALD.forwardKlDerivativeSideConditionContract, SALD.generalMovingTargetDerivativeCandidateContract, and sald.general_moving_target.kl_derivative keep density/law regularity, mass conservation, integration by parts, target transport, sigma positivity, and inverse-schedule side conditions explicit.",
    "Five-backend check 5, EM interpolation Fokker-Planck: SALD.discreteForwardKlEmInterpolationSideConditionContract, SALD.generalMovingTargetDiscreteDerivativeSideConditionContract, SALD.cycle48GeneralMovingTargetDiscreteEmEndpointFpAuditObligation, and sald.general_moving_target_discrete.em_interpolation_fp expose endpoint laws, conditional drift, conditional-law density/absolute-continuity, weak Fokker-Planck, Laplacian split, and stitched-interval interfaces for downstream discrete reuse.",
    "The theorem route check remains in paper order: forward-KL through cycle 60, discrete forward-KL through cycle 61, guided residual through the normalizer and identity obligations, general moving-target through derivative/LSI/DV/Gronwall/pure-contraction interfaces, unified forward-KL as the c_t<-u_t specialization, and discrete general moving-target through the existing EM/frozen-delta/LSI/DV/Gronwall interfaces.",
    "FaithfulPaper Phase 1: use appendix.tex:619-951 and the original main_body.tex unified reference only; sald_version_2.tex remains excluded."
  ]
  nonGoals := [
    "Do not restate prop:guided_path_residual, thm:general-moving-target-SALD, thm:unified-forward-KL, or any theorem display.",
    "Do not add hidden density, endpoint, common-space, finite-log-mgf, sigma-positivity, schedule, or coefficient-regularity assumptions to the source theorem statements.",
    "Do not promote guided residual calculus, Fokker-Planck/KL differentiation, LSI/KL/FI, DV, Gronwall, pure contraction, EM interpolation, or any theorem status above contractOnly/sourceCited/obligation.",
    "Do not replace the source route by a direct VA-SALD proof, path-space comparison, Girsanov, Pinsker, Talagrand, PI, or SLT-based proof.",
    "Do not begin systematic measure-theory or SDE backfill in this upper cycle; missing analytic facts must stay as source-cited interfaces or obligations."
  ]
  lowerPacket := [
    "Middle should synchronize this cycle-62 upper route with conversion-windows/ASTIS-SALD-001.md, proof-obligations/ASTIS-SALD-001.md, and the guided/general proof DAG before lower proof search.",
    "Lower route audit target: appendix.tex:619-951, checking that every guided residual and general moving-target proof step maps to SALD.guidedResidualIdentityContract, SALD.generalMovingTargetDerivativeCandidateContract, SALD.saldLsiKlFiDensityTestContract, SALD.generalMovingTargetDvFiniteLogMgfWitnessContract, SALD.generalMovingTargetGronwallSideConditionContract, or a named obligation.",
    "After the route audit is accepted, proof-producing lower work should target exactly SALD.generalMovingTargetDerivativeCandidateContract / SALD.generalMovingTargetDerivativeObligation / sald.general_moving_target.kl_derivative over appendix.tex:765-884.",
    "First derivative sub-slice: appendix.tex:765-812, exposing law regularity, mass conservation, KL differentiation under the integral, the general moving-target Fokker-Planck equation, and integration-by-parts side conditions.",
    "Second derivative sub-slice: appendix.tex:813-864, exposing target transport by v_t, rescaled transport of pi_{t(s)}, residual m_t=v_t-c_t, and Young with epsilon=2*dot t(s)/sigma_{t(s)}^2.",
    "Third derivative sub-slice: appendix.tex:865-884, preserving the LSI handoff and s-to-t schedule/sigma side conditions without adding them to the theorem statement.",
    "Leave guided normalizer differentiation, residual DV finite-log-mgf, Gronwall endpoint/exponent, pure contraction, unified specialization, and downstream EM interpolation as separate obligations unless exact compiled proofs are added."
  ]
  reviewerChecklist := [
    "The cycle-62 route uses cycle 61 as the recovered discrete forward-KL prerequisite and does not reopen the cycle-56 failure.",
    "SALD.guidedResidualContract and SALD.generalVaSaldContract list SALD.cycle62GuidedGeneralSkeletonObligation while remaining contractOnly.",
    "SALD.generalVaSaldProofDag contains ASTIS.SALD.guided_general.cycle62_global_phase_judgment, cycle62_five_backend_check, cycle62_upper_route, and the selected lower-packet node.",
    "SALD.saldDependenciesForLabel for prop:guided_path_residual and thm:general-moving-target-SALD includes the cycle-62 packet, obligation, and DAG nodes.",
    "The five slow analytic interfaces remain source-cited or obligation-level; no source theorem statement, source constant, source label, SLT reuse status, or analytic backend status changes.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  status := ProofStatus.obligation

/-- Cycle-62 upper obligation tying the guided/general theorem route to the
accepted cycle-61 recovery and the five explicit analytic backend interfaces. -/