AutoSamplingTheory.SALD.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperPacket

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 cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperPacket :
    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 85 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, and the single packet that now reduces the largest proof risk is the generator-to-law weak Fokker-Planck boundary at appendix.tex:1379-1387. Lower should use the cycle-79 lawMapIntegral helpers and the cycle-85 named conditional-integral regularity progress to discharge or sharply narrow the supplied generator/time-derivative hypothesis consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff.

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. sald.general_moving_target_discrete.em_interpolation_fp
3. sald.general_moving_target_discrete.cycle86_weak_fp_generator_boundary_upper
4. AutoSamplingTheory.lawMapIntegral
5. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
7. thm:forward-KL-discrete
8. 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. The active packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed in this cycle to appendix.tex:1379-1387.
2. Cycle 79 already formalized the Measure.map weak-test integral rewrite and the supplied sample-space HasDerivAt transport; lower should build on AutoSamplingTheory.lawMapIntegral and AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample instead of restating them.
3. Cycle 85 discharged the generic component-field measurability/integrability sub-hypothesis when the SALD fields are chosen as hatRhoS-a.e. versions of canonical condDistrib integrals; lower may use that as the drift-regularity dependency but must not reopen broad conditional-law work.
4. The target supplied hypothesis to remove or narrow is the generator/time-derivative input in the cycle-77/cycle-82 weak-FP wrappers: partialS phi equals the frozen EM generator action for admissible tests.
5. If the full generator theorem is too large, lower should record the smallest remaining named theorem, such as sample-path generator differentiation, Bochner/parametric integral interchange, or conditional-drift source-action identification, with imports and hypotheses explicit.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. Preserve appendix.tex:1379-1387: the paper invokes the Fokker-Planck equation associated with eq:general_moving_target_SALD_frozen_interp and obtains partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + (sigma_eta^2/2)*Delta hat rho_s.
2. 2. Work before the existing source-sign wrappers: derive or narrow the weak-test generator-to-law statement that supplies partialS phi = generatorAction phi.
3. 3. Use Measure.map transport to move between the law integral over hat rho_s=Law(hat X_s) and the sample-space integral over hat X_s.
4. 4. Keep drift/diffusion source signs, KL/log-ratio substitution, integration by parts, FI identification, LSI, DV, Gronwall, and theorem closure as downstream consumers.

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 appendix.tex:1379-1387 source statement, the sign of the drift term, the sigma_eta^2/2 diffusion coefficient, and both discrete theorem statements.
2. Do not add generator, density, boundary, conditional-law, or admissible-test assumptions to theorem statements; any such hypotheses belong only in the local backend theorem boundary.
3. Use lean-stat-learning-theory only as a reference for Mathlib measure/probability style; do not import it, change Lake dependencies, or mark an SLT theorem formalized.

nonGoals : List String (explicit)

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

Ordered data items

1. No theorem-route audit, broad source-index rebaseline, display algebra, Gronwall/DV/LSI/frozen-delta work, KL/log-ratio work, reusable API redesign, or project-article export.
2. No new supplied-hypothesis wrapper unless it removes an older supplied generator/time-derivative, source-action, or integrability hypothesis, or names a strictly smaller missing theorem.
3. No status promotion for sald.general_moving_target_discrete.em_interpolation_fp, sald.discrete_forward_kl.em_interpolation_fp, weak FP, KL derivative, 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 the generator-to-law weak-FP boundary at appendix.tex:1379-1387.
2. Preferred product: a compiled local theorem using AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample and Mathlib parametric/Bochner integral APIs that removes the supplied hgenerator-style hypothesis for admissible weak tests, or a strict subcase of it.
3. Allowed blocked product: one precise source-cited theorem boundary naming the missing Mathlib/local theorem, imports, and hypotheses for sample-path generator differentiation, parametric integral interchange, or drift/diffusion source-action identification.
4. Classification required in the lower handoff: discharges-supplied-hypothesis, narrows-source-cited-boundary, or rejected-wrapper-churn.

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 and the sub-slice appendix.tex:1379-1387.
2. Reject a packet that only repackages the cycle-77/cycle-82 supplied hypotheses without removing hgenerator, source-action, or a smaller named theorem boundary.
3. Check that Measure.map and Bochner/parametric-integral transport is used in the direction law integral to sample-space integral and back, consistent with AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample.
4. Preserve the source signs -div(hat rho_s*bar b_{k,s}) and +(sigma_eta^2/2)*Delta hat rho_s; do not change constants or source labels.
5. No theorem status, EM backend status, SLT status, or Lake dependency is promoted.
6. 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.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation
3. AutoSamplingTheory.lawMapIntegral
4. AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample
5. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
7. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
8. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff
9. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
10. SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation
11. AutoSamplingTheory.condDistribIntegralNamedFieldRegularity
12. Mathlib.Analysis.Calculus.ParametricIntegral
13. Mathlib.MeasureTheory.Integral.Bochner.Basic
14. sald.general_moving_target_discrete.em_interpolation_fp
15. 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 cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteWeakFpSource
  objective := "Global phase judgment: cycle 85 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, and the single packet that now reduces the largest proof risk is the generator-to-law weak Fokker-Planck boundary at appendix.tex:1379-1387. Lower should use the cycle-79 lawMapIntegral helpers and the cycle-85 named conditional-integral regularity progress to discharge or sharply narrow the supplied generator/time-derivative hypothesis consumed by SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff."
  sourceLabels := [
    "proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.cycle86_weak_fp_generator_boundary_upper",
    "AutoSamplingTheory.lawMapIntegral",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "The active packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed in this cycle to appendix.tex:1379-1387.",
    "Cycle 79 already formalized the Measure.map weak-test integral rewrite and the supplied sample-space HasDerivAt transport; lower should build on AutoSamplingTheory.lawMapIntegral and AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample instead of restating them.",
    "Cycle 85 discharged the generic component-field measurability/integrability sub-hypothesis when the SALD fields are chosen as hatRhoS-a.e. versions of canonical condDistrib integrals; lower may use that as the drift-regularity dependency but must not reopen broad conditional-law work.",
    "The target supplied hypothesis to remove or narrow is the generator/time-derivative input in the cycle-77/cycle-82 weak-FP wrappers: partialS phi equals the frozen EM generator action for admissible tests.",
    "If the full generator theorem is too large, lower should record the smallest remaining named theorem, such as sample-path generator differentiation, Bochner/parametric integral interchange, or conditional-drift source-action identification, with imports and hypotheses explicit."
  ]
  theoremRoute := [
    "1. Preserve appendix.tex:1379-1387: the paper invokes the Fokker-Planck equation associated with eq:general_moving_target_SALD_frozen_interp and obtains partial_s hat rho_s = -div(hat rho_s*bar b_{k,s}) + (sigma_eta^2/2)*Delta hat rho_s.",
    "2. Work before the existing source-sign wrappers: derive or narrow the weak-test generator-to-law statement that supplies partialS phi = generatorAction phi.",
    "3. Use Measure.map transport to move between the law integral over hat rho_s=Law(hat X_s) and the sample-space integral over hat X_s.",
    "4. Keep drift/diffusion source signs, KL/log-ratio substitution, integration by parts, FI identification, LSI, DV, Gronwall, and theorem closure as downstream consumers."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: preserve the appendix.tex:1379-1387 source statement, the sign of the drift term, the sigma_eta^2/2 diffusion coefficient, and both discrete theorem statements.",
    "Do not add generator, density, boundary, conditional-law, or admissible-test assumptions to theorem statements; any such hypotheses belong only in the local backend theorem boundary.",
    "Use lean-stat-learning-theory only as a reference for Mathlib measure/probability style; do not import it, change Lake dependencies, or mark an SLT theorem formalized."
  ]
  nonGoals := [
    "No theorem-route audit, broad source-index rebaseline, display algebra, Gronwall/DV/LSI/frozen-delta work, KL/log-ratio work, reusable API redesign, or project-article export.",
    "No new supplied-hypothesis wrapper unless it removes an older supplied generator/time-derivative, source-action, or integrability hypothesis, or names a strictly smaller missing theorem.",
    "No status promotion for sald.general_moving_target_discrete.em_interpolation_fp, sald.discrete_forward_kl.em_interpolation_fp, weak FP, KL derivative, 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 the generator-to-law weak-FP boundary at appendix.tex:1379-1387.",
    "Preferred product: a compiled local theorem using AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample and Mathlib parametric/Bochner integral APIs that removes the supplied hgenerator-style hypothesis for admissible weak tests, or a strict subcase of it.",
    "Allowed blocked product: one precise source-cited theorem boundary naming the missing Mathlib/local theorem, imports, and hypotheses for sample-path generator differentiation, parametric integral interchange, or drift/diffusion source-action identification.",
    "Classification required in the lower handoff: discharges-supplied-hypothesis, narrows-source-cited-boundary, or rejected-wrapper-churn."
  ]
  reviewerChecklist := [
    "The active packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 and the sub-slice appendix.tex:1379-1387.",
    "Reject a packet that only repackages the cycle-77/cycle-82 supplied hypotheses without removing hgenerator, source-action, or a smaller named theorem boundary.",
    "Check that Measure.map and Bochner/parametric-integral transport is used in the direction law integral to sample-space integral and back, consistent with AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample.",
    "Preserve the source signs -div(hat rho_s*bar b_{k,s}) and +(sigma_eta^2/2)*Delta hat rho_s; do not change constants or source labels.",
    "No theorem status, EM backend status, SLT status, or Lake dependency is promoted.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureLowerObligation",
    "AutoSamplingTheory.lawMapIntegral",
    "AutoSamplingTheory.lawMapIntegralHasDerivAtOfSample",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfReadinessAndGeneratorPiecesHandoff",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
    "SALD.cycle85GeneralMovingTargetDiscreteConditionalKernelBoundaryLowerObligation",
    "AutoSamplingTheory.condDistribIntegralNamedFieldRegularity",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  status := ProofStatus.obligation

/-- Cycle-86 upper obligation selecting the generator-to-law weak FP boundary. -/