AutoSamplingTheory.SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperPacket

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 cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperPacket :
    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.saldGeneralMovingTargetDiscreteWeakFpSource — 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.

Global phase judgment: cycle 81 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet that best reduces the remaining proof risk is the weak conditional Fokker-Planck source-sign statement inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, specifically appendix.tex:1379-1387 after the cycle-81 endpoint/conditional WeakFpPrereq readiness package.

sourceLabels : List String (explicit)

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

Ordered data items

1. proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp
2. proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.general_moving_target_discrete.cycle82_weak_fp_source_signs_upper
5. thm:forward-KL-discrete
6. thm:general-moving-target-SALD-discrete

analyticInterfaces : List String (explicit)

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

Ordered data items

1. Cycle 81 accepted only endpoint Measure.map and bar b_{k,s} readiness for a supplied WeakFpPrereq consumer; it did not prove the weak FP theorem, density/AC, generator theorem, or KL derivative.
2. The active source line is appendix.tex:1379-1387: partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + (sigma_eta^2/2)*Delta hat rho_s.
3. Existing cycle-72 and cycle-77 wrappers preserve the negative drift-divergence sign and positive sigma_eta^2/2 Laplacian coefficient once the analytic weak-test or generator identity is supplied.
4. Cycle 82 asks middle/lower to connect the cycle-81 readiness boundary to that supplied weak-test source-sign theorem with all hypotheses explicit, not to broaden the theorem route.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. Stay on the fixed interval k, s in [s_k,s_{k+1}] inside appendix.tex:1358-1387.
2. 2. Use cycle-81 endpoint/conditional readiness for the named law hat rho_s, kernel orientation, and bar b_{k,s} measurability/integrability.
3. 3. State the weak conditional FP source-sign theorem over an admissible test class: partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi.
4. 4. If using generator pieces, keep the supplied hypotheses separated as generator/time-derivative, generator split, drift source action, diffusion source action, boundary behavior, and sigmaCoeff=sigma_eta^2/2.
5. 5. Leave log-ratio admissibility, KL differentiation, Laplacian split, integration by parts, FI identification, LSI/KL/FI, DV, Gronwall, and theorem closure downstream.

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1 only: preserve appendix.tex:1379-1387 and keep sald_version_2.tex out of scope.
2. Do not add conditional-law, density, admissible-test, boundary, finite-FI, or generator assumptions to theorem statements; keep them in source-cited interfaces or obligations.
3. Use lean-stat-learning-theory only as a local Mathlib style reference; do not import it, change Lake dependencies, or claim an SLT theorem is formalized.

nonGoals : List String (explicit)

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

Ordered data items

1. No theorem-route audit, display algebra, source-index rebaseline beyond the gate, KL-derivative proof, Gronwall/DV/LSI work, frozen-delta work, broad reusable API design, or project-article export.
2. No proof of the full EM/Brownian construction, regular conditional law, density/absolute-continuity, generator theorem, weak FP theorem, or integration-by-parts theorem unless it is compiled locally in this exact backend.
3. No status promotion for sald.general_moving_target_discrete.em_interpolation_fp, sald.discrete_forward_kl.em_interpolation_fp, either discrete theorem contract, SLT reuse, or Lake dependencies.

lowerPacket : List String (explicit)

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

Ordered data items

1. Target exactly sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1379-1387 weak FP source signs.
2. Middle compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff, translating the cycle-81 WeakFpPrereq readiness output into the lower-ready hypotheses consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff.
3. Lower should compile only a supplied-hypothesis bridge from WeakFpPrereq, generator/time-derivative, drift source action, diffusion source action, and sigmaCoeff=sigma_eta^2/2 to the normalized source signs, if feasible.
4. If blocked, record one exact missing Mathlib/SDE theorem boundary for the weak generator-to-law statement, with common-space, conditional kernel, density/time regularity, admissible tests, boundary behavior, and coefficient hypotheses explicit.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. The active packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, specifically appendix.tex:1379-1387.
2. The drift sign remains negative -div(hat rho_s*bar b_{k,s}) and the diffusion sign remains positive +(sigma_eta^2/2)*Delta hat rho_s.
3. Cycle 82 reuses cycle-81 readiness, cycle-72 source-sign wrappers, cycle-77 generator-piece wrappers, and cycle-79 source-cited measure interface instead of duplicating or promoting them.
4. Both discrete theorem contracts remain contractOnly; conditional law, weak FP, generator-to-law, KL derivative, density/AC, LSI/KL/FI, DV, and Gronwall remain sourceCited or obligation unless a local declaration compiles.
5. SLT remains reference-only with no Lake dependency or import change, and python3 tools/astis.py source-index ASTIS-SALD-001 plus 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.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
2. SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff
3. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
4. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff
7. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
8. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
9. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
10. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff
11. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
12. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
13. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
14. SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation
15. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
16. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
17. sald.general_moving_target_discrete.em_interpolation_fp
18. sald.discrete_forward_kl.em_interpolation_fp

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 cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteWeakFpSource
  objective := "Global phase judgment: cycle 81 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet that best reduces the remaining proof risk is the weak conditional Fokker-Planck source-sign statement inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, specifically appendix.tex:1379-1387 after the cycle-81 endpoint/conditional WeakFpPrereq readiness package."
  sourceLabels := [
    "proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp",
    "proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.cycle82_weak_fp_source_signs_upper",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Cycle 81 accepted only endpoint Measure.map and bar b_{k,s} readiness for a supplied WeakFpPrereq consumer; it did not prove the weak FP theorem, density/AC, generator theorem, or KL derivative.",
    "The active source line is appendix.tex:1379-1387: partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + (sigma_eta^2/2)*Delta hat rho_s.",
    "Existing cycle-72 and cycle-77 wrappers preserve the negative drift-divergence sign and positive sigma_eta^2/2 Laplacian coefficient once the analytic weak-test or generator identity is supplied.",
    "Cycle 82 asks middle/lower to connect the cycle-81 readiness boundary to that supplied weak-test source-sign theorem with all hypotheses explicit, not to broaden the theorem route."
  ]
  theoremRoute := [
    "1. Stay on the fixed interval k, s in [s_k,s_{k+1}] inside appendix.tex:1358-1387.",
    "2. Use cycle-81 endpoint/conditional readiness for the named law hat rho_s, kernel orientation, and bar b_{k,s} measurability/integrability.",
    "3. State the weak conditional FP source-sign theorem over an admissible test class: partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi.",
    "4. If using generator pieces, keep the supplied hypotheses separated as generator/time-derivative, generator split, drift source action, diffusion source action, boundary behavior, and sigmaCoeff=sigma_eta^2/2.",
    "5. Leave log-ratio admissibility, KL differentiation, Laplacian split, integration by parts, FI identification, LSI/KL/FI, DV, Gronwall, and theorem closure downstream."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: preserve appendix.tex:1379-1387 and keep sald_version_2.tex out of scope.",
    "Do not add conditional-law, density, admissible-test, boundary, finite-FI, or generator assumptions to theorem statements; keep them in source-cited interfaces or obligations.",
    "Use lean-stat-learning-theory only as a local Mathlib style reference; do not import it, change Lake dependencies, or claim an SLT theorem is formalized."
  ]
  nonGoals := [
    "No theorem-route audit, display algebra, source-index rebaseline beyond the gate, KL-derivative proof, Gronwall/DV/LSI work, frozen-delta work, broad reusable API design, or project-article export.",
    "No proof of the full EM/Brownian construction, regular conditional law, density/absolute-continuity, generator theorem, weak FP theorem, or integration-by-parts theorem unless it is compiled locally in this exact backend.",
    "No status promotion for sald.general_moving_target_discrete.em_interpolation_fp, sald.discrete_forward_kl.em_interpolation_fp, either discrete theorem contract, SLT reuse, or Lake dependencies."
  ]
  lowerPacket := [
    "Target exactly sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1379-1387 weak FP source signs.",
    "Middle compiles SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff, translating the cycle-81 WeakFpPrereq readiness output into the lower-ready hypotheses consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff.",
    "Lower should compile only a supplied-hypothesis bridge from WeakFpPrereq, generator/time-derivative, drift source action, diffusion source action, and sigmaCoeff=sigma_eta^2/2 to the normalized source signs, if feasible.",
    "If blocked, record one exact missing Mathlib/SDE theorem boundary for the weak generator-to-law statement, with common-space, conditional kernel, density/time regularity, admissible tests, boundary behavior, and coefficient hypotheses explicit."
  ]
  reviewerChecklist := [
    "The active packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, specifically appendix.tex:1379-1387.",
    "The drift sign remains negative -div(hat rho_s*bar b_{k,s}) and the diffusion sign remains positive +(sigma_eta^2/2)*Delta hat rho_s.",
    "Cycle 82 reuses cycle-81 readiness, cycle-72 source-sign wrappers, cycle-77 generator-piece wrappers, and cycle-79 source-cited measure interface instead of duplicating or promoting them.",
    "Both discrete theorem contracts remain contractOnly; conditional law, weak FP, generator-to-law, KL derivative, density/AC, LSI/KL/FI, DV, and Gronwall remain sourceCited or obligation unless a local declaration compiles.",
    "SLT remains reference-only with no Lake dependency or import change, and python3 tools/astis.py source-index ASTIS-SALD-001 plus python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
    "SALD.generalMovingTargetDiscreteEndpointMeasureMapWeakFpPrereqHandoff",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
    "SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation",
    "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  status := ProofStatus.obligation

/-- Cycle-82 upper obligation selecting the weak conditional FP source-sign
packet after the endpoint/conditional readiness work. -/