AutoSamplingTheory.SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperPacket

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 cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperPacket :
    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 78 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; proof-producing equality wrappers have reached the supplied-hypothesis boundary, so the single lower packet that now reduces the largest proof risk is the narrow source-cited weak generator-to-law time-derivative interface for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.

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.cycle79_weak_fp_generator_measure_interface
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. Gronwall, DV, LSI/KL/FI, and continuous Fokker-Planck/KL derivative interfaces remain unchanged and below formalized status.
2. Cycles 70-76 exposed the conditional-law, endpoint, and kernel-orientation layers; cycle 74 remains the source-cited conditional-kernel measure interface.
3. Cycles 77-78 compile only supplied-hypothesis wrappers from generator pieces to weak FP source signs and then to the KL derivative display.
4. Cycle 79 names the remaining blocked theorem: differentiating the EM interpolation Measure.map law/test integral and identifying the generator action before any integration by parts, FI identification, LSI, DV, or Gronwall step.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. Stay inside appendix.tex:1358-1387 and keep the active backend sald.general_moving_target_discrete.em_interpolation_fp.
2. 2. Use appendix.tex:1379-1387 as the selected lower slice: the paper invokes the Fokker-Planck equation associated with eq:general_moving_target_SALD_frozen_interp.
3. 3. Expose the missing measure/calculus theorem as a source-cited interface: for admissible weak tests, differentiate the law/test integral for hat rho_s and identify the frozen EM generator with drift bar b_{k,s} and covariance sigma_eta^2.
4. 4. Leave all later KL substitution, Laplacian split, FI, LSI, DV, and Gronwall work as consumers of this interface, not as replacements for it.

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1 only: preserve the original appendix.tex source route and keep sald_version_2.tex excluded.
2. Do not add the law differentiability, generator, density, boundary, or admissible-test assumptions to theorem statements; record them in this interface.
3. Do not claim a Mathlib, SLT, or local SDE theorem is formalized unless a local ASTIS declaration compiles under this toolchain.

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, Gronwall/DV/LSI work, frozen-delta work, broad reusable API design, or project-article export.
2. No new Lake dependency and no SLT import or formalization claim.
3. No promotion of the EM interpolation FP, weak FP theorem, KL derivative backend, or theorem contracts.

lowerPacket : List String (explicit)

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

Ordered data items

1. Target exactly SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface / sald.general_moving_target_discrete.cycle79_weak_fp_generator_measure_interface.
2. Middle should synchronize appendix.tex:1379-1387 with the already named cycle-77 generator/time-derivative and generator-piece hypotheses, and make clear that cycle 79 records the theorem boundary before those wrappers.
3. Lower should either find a tiny local measure/calculus wrapper around Measure.map integrals and parametric integral differentiation under explicit supplied hypotheses, or keep this sourceCited interface as the blocker; do not switch to theorem-route, display, DV, LSI, or Gronwall work.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. The active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1379-1387.
2. The new weak generator-to-law interface is ProofStatus.sourceCited and does not claim that Mathlib contains a full SDE/Fokker-Planck theorem.
3. Cycle 77 and 78 wrappers remain local supplied-hypothesis packaging only.
4. Both discrete theorem contracts remain contractOnly, and all slow analytic backends remain obligation or sourceCited.
5. python3 tools/astis.py source-index ASTIS-SALD-001 and 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.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
5. SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
6. SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation
7. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
8. sald.general_moving_target_discrete.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 cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteWeakFpSource
  objective := "Global phase judgment: cycle 78 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; proof-producing equality wrappers have reached the supplied-hypothesis boundary, so the single lower packet that now reduces the largest proof risk is the narrow source-cited weak generator-to-law time-derivative interface for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387."
  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.cycle79_weak_fp_generator_measure_interface",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Gronwall, DV, LSI/KL/FI, and continuous Fokker-Planck/KL derivative interfaces remain unchanged and below formalized status.",
    "Cycles 70-76 exposed the conditional-law, endpoint, and kernel-orientation layers; cycle 74 remains the source-cited conditional-kernel measure interface.",
    "Cycles 77-78 compile only supplied-hypothesis wrappers from generator pieces to weak FP source signs and then to the KL derivative display.",
    "Cycle 79 names the remaining blocked theorem: differentiating the EM interpolation Measure.map law/test integral and identifying the generator action before any integration by parts, FI identification, LSI, DV, or Gronwall step."
  ]
  theoremRoute := [
    "1. Stay inside appendix.tex:1358-1387 and keep the active backend sald.general_moving_target_discrete.em_interpolation_fp.",
    "2. Use appendix.tex:1379-1387 as the selected lower slice: the paper invokes the Fokker-Planck equation associated with eq:general_moving_target_SALD_frozen_interp.",
    "3. Expose the missing measure/calculus theorem as a source-cited interface: for admissible weak tests, differentiate the law/test integral for hat rho_s and identify the frozen EM generator with drift bar b_{k,s} and covariance sigma_eta^2.",
    "4. Leave all later KL substitution, Laplacian split, FI, LSI, DV, and Gronwall work as consumers of this interface, not as replacements for it."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: preserve the original appendix.tex source route and keep sald_version_2.tex excluded.",
    "Do not add the law differentiability, generator, density, boundary, or admissible-test assumptions to theorem statements; record them in this interface.",
    "Do not claim a Mathlib, SLT, or local SDE theorem is formalized unless a local ASTIS declaration compiles under this toolchain."
  ]
  nonGoals := [
    "No theorem-route audit, display algebra, Gronwall/DV/LSI work, frozen-delta work, broad reusable API design, or project-article export.",
    "No new Lake dependency and no SLT import or formalization claim.",
    "No promotion of the EM interpolation FP, weak FP theorem, KL derivative backend, or theorem contracts."
  ]
  lowerPacket := [
    "Target exactly SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface / sald.general_moving_target_discrete.cycle79_weak_fp_generator_measure_interface.",
    "Middle should synchronize appendix.tex:1379-1387 with the already named cycle-77 generator/time-derivative and generator-piece hypotheses, and make clear that cycle 79 records the theorem boundary before those wrappers.",
    "Lower should either find a tiny local measure/calculus wrapper around Measure.map integrals and parametric integral differentiation under explicit supplied hypotheses, or keep this sourceCited interface as the blocker; do not switch to theorem-route, display, DV, LSI, or Gronwall work."
  ]
  reviewerChecklist := [
    "The active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1379-1387.",
    "The new weak generator-to-law interface is ProofStatus.sourceCited and does not claim that Mathlib contains a full SDE/Fokker-Planck theorem.",
    "Cycle 77 and 78 wrappers remain local supplied-hypothesis packaging only.",
    "Both discrete theorem contracts remain contractOnly, and all slow analytic backends remain obligation or sourceCited.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
    "SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  status := ProofStatus.obligation

/-- Cycle-79 upper obligation for the weak generator-to-law cited interface. -/