AutoSamplingTheory.SALD.cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddlePacket

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 cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddlePacket :
    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.saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource — 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.

Cycle 88 middle: cycle 87 was accepted and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the active packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1358-1366. The single lower packet is the log-ratio weak-test admissibility/smoothing boundary: replace the supplied hlog hypothesis used by the cycle-83/cycle-84 weak-FP-to-KL handoffs with a narrower source-cited theorem boundary using cycle-87 finite-KL llr regularity.

sourceLabels : List String (explicit)

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

Ordered data items

1. eq:general_KL_derivative_0_discrete
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.kl_derivative
5. sald.general_moving_target_discrete.cycle88_kl_log_ratio_admissibility_middle
6. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
7. SALD.GeneralMovingTargetDiscreteKlLogRatioAdmissibilityClosure
8. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
9. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
10. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
11. thm:forward-KL-discrete
12. 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. Selected supplied hypothesis to reduce: hlog : Admissible logRatioTest in the cycle-83/cycle-84 weak-FP-to-KL handoffs.
2. Cycle 87 already turns finite KL into hatRhoS << tildePiS plus AEStronglyMeasurable and Integrable llr; do not restate those as separate supplied hypotheses.
3. Remaining admissibility theorem: the Mathlib llr representative is admitted by the weak-FP test class after smoothing/Sobolev approximation, boundary/no-flux control, and closure of weak-FP actions under that approximation.
4. The lower boundary must name the density/time regularity, zero-set convention, finite action, drift-divergence action, Laplacian action, and target-time integrability hypotheses that make the approximation legitimate.
5. Classification for this middle packet: narrows-source-cited-boundary. It is not a proof of weak FP, KL differentiability, integration by parts, or FI identification.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. Use appendix.tex:1358-1366 to keep the log-density-ratio test at the KL derivative step.
2. 2. Replace the old generic hlog assumption by the smaller admissibility theorem for llr hatRhoS tildePiS under finite KL regularity plus approximation/closure hypotheses.
3. 3. Feed the resulting admissible test into the existing cycle-87 raw-KL/mass split and cycle-83/cycle-84 source-sign handoffs.
4. 4. Leave raw KL differentiability, mass conservation, target-time derivative, weak FP, integration by parts, and FI identification as downstream obligations.

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:1358-1366, eq:general_KL_derivative_0_discrete, the target-time minus sign, and both discrete theorem statements.
2. Do not add an admissibility assumption to thm:forward-KL-discrete or thm:general-moving-target-SALD-discrete; keep it inside the EM/KL backend boundary.
3. Use Mathlib/local ASTIS declarations only; lean-stat-learning-theory remains a reference and is not a Lake dependency.

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/frozen-delta work, conditional-kernel work, generator-to-law weak-FP work, reusable API redesign, or project-article export.
2. No new supplied-hypothesis wrapper around hlog unless it removes that older hlog dependency or names the smaller approximation/closure theorem precisely.
3. No status promotion for sald.general_moving_target_discrete.em_interpolation_fp, sald.discrete_forward_kl.em_interpolation_fp, sald.general_moving_target_discrete.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 the log-ratio admissibility boundary at appendix.tex:1358-1366.
2. Preferred product: a compiled theorem deriving Admissible (llr hatRhoS tildePiS) from finite KL, density/time regularity, a smooth/Sobolev approximation sequence, boundary/no-flux control, and weak-FP action closure.
3. Allowed blocked product: one precise source-cited theorem boundary naming the missing approximation/closure theorem and the imports/hypotheses needed to replace hlog.
4. Cycle 88 lower product: SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure derives Admissible (llr hatRhoS tildePiS) from finite KL and the named approximation/closure package, so the broad hlog is replaced by the smaller closure theorem boundary.
5. Classification required: discharges-supplied-hypothesis if hlog is actually removed by a compiled theorem; otherwise narrows-source-cited-boundary if the smaller theorem is recorded; rejected-wrapper-churn for another hlog wrapper.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. The packet targets appendix.tex:1358-1366 and the active EM backend over appendix.tex:1358-1387.
2. The supplied hypothesis being reduced is exactly hlog : Admissible logRatioTest, not raw KL differentiability or weak FP.
3. Cycle 87 finite-KL llr regularity is used as a dependency; AC/measurability/integrability should not be reintroduced as separate supplied hypotheses.
4. The missing theorem names smoothing/Sobolev approximation, boundary behavior, weak-FP action closure, density/time regularity, and zero-set convention.
5. No theorem status, EM/KL 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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation
2. SALD.generalMovingTargetDiscreteKlLogRatioLlrDef
3. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
4. SALD.GeneralMovingTargetDiscreteKlLogRatioAdmissibilityClosure
5. SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction
7. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
8. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
9. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
10. Mathlib.InformationTheory.KullbackLeibler.Basic
11. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
12. Mathlib.MeasureTheory.Integral.Bochner.Basic
13. Mathlib.Analysis.Calculus.ParametricIntegral
14. eq:general_KL_derivative_0_discrete
15. sald.general_moving_target_discrete.em_interpolation_fp
16. sald.discrete_forward_kl.em_interpolation_fp
17. sald.general_moving_target_discrete.kl_derivative

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 cycle88GeneralMovingTargetDiscreteKlLogRatioAdmissibilityMiddlePacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Cycle 88 middle: cycle 87 was accepted and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the active packet remains sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1358-1366.  The single lower packet is the log-ratio weak-test admissibility/smoothing boundary: replace the supplied hlog hypothesis used by the cycle-83/cycle-84 weak-FP-to-KL handoffs with a narrower source-cited theorem boundary using cycle-87 finite-KL llr regularity."
  sourceLabels := [
    "eq:general_KL_derivative_0_discrete",
    "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.kl_derivative",
      "sald.general_moving_target_discrete.cycle88_kl_log_ratio_admissibility_middle",
      "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
      "SALD.GeneralMovingTargetDiscreteKlLogRatioAdmissibilityClosure",
      "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
      "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
      "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
      "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Selected supplied hypothesis to reduce: hlog : Admissible logRatioTest in the cycle-83/cycle-84 weak-FP-to-KL handoffs.",
    "Cycle 87 already turns finite KL into hatRhoS << tildePiS plus AEStronglyMeasurable and Integrable llr; do not restate those as separate supplied hypotheses.",
    "Remaining admissibility theorem: the Mathlib llr representative is admitted by the weak-FP test class after smoothing/Sobolev approximation, boundary/no-flux control, and closure of weak-FP actions under that approximation.",
    "The lower boundary must name the density/time regularity, zero-set convention, finite action, drift-divergence action, Laplacian action, and target-time integrability hypotheses that make the approximation legitimate.",
    "Classification for this middle packet: narrows-source-cited-boundary. It is not a proof of weak FP, KL differentiability, integration by parts, or FI identification."
  ]
  theoremRoute := [
    "1. Use appendix.tex:1358-1366 to keep the log-density-ratio test at the KL derivative step.",
    "2. Replace the old generic hlog assumption by the smaller admissibility theorem for llr hatRhoS tildePiS under finite KL regularity plus approximation/closure hypotheses.",
    "3. Feed the resulting admissible test into the existing cycle-87 raw-KL/mass split and cycle-83/cycle-84 source-sign handoffs.",
    "4. Leave raw KL differentiability, mass conservation, target-time derivative, weak FP, integration by parts, and FI identification as downstream obligations."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: preserve appendix.tex:1358-1366, eq:general_KL_derivative_0_discrete, the target-time minus sign, and both discrete theorem statements.",
    "Do not add an admissibility assumption to thm:forward-KL-discrete or thm:general-moving-target-SALD-discrete; keep it inside the EM/KL backend boundary.",
    "Use Mathlib/local ASTIS declarations only; lean-stat-learning-theory remains a reference and is not a Lake dependency."
  ]
  nonGoals := [
    "No theorem-route audit, display algebra, Gronwall/DV/LSI/frozen-delta work, conditional-kernel work, generator-to-law weak-FP work, reusable API redesign, or project-article export.",
    "No new supplied-hypothesis wrapper around hlog unless it removes that older hlog dependency or names the smaller approximation/closure theorem precisely.",
    "No status promotion for sald.general_moving_target_discrete.em_interpolation_fp, sald.discrete_forward_kl.em_interpolation_fp, sald.general_moving_target_discrete.kl_derivative, either discrete theorem contract, SLT reuse, or Lake dependencies."
  ]
  lowerPacket := [
    "Target exactly the log-ratio admissibility boundary at appendix.tex:1358-1366.",
    "Preferred product: a compiled theorem deriving Admissible (llr hatRhoS tildePiS) from finite KL, density/time regularity, a smooth/Sobolev approximation sequence, boundary/no-flux control, and weak-FP action closure.",
      "Allowed blocked product: one precise source-cited theorem boundary naming the missing approximation/closure theorem and the imports/hypotheses needed to replace hlog.",
      "Cycle 88 lower product: SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure derives Admissible (llr hatRhoS tildePiS) from finite KL and the named approximation/closure package, so the broad hlog is replaced by the smaller closure theorem boundary.",
      "Classification required: discharges-supplied-hypothesis if hlog is actually removed by a compiled theorem; otherwise narrows-source-cited-boundary if the smaller theorem is recorded; rejected-wrapper-churn for another hlog wrapper."
    ]
  reviewerChecklist := [
    "The packet targets appendix.tex:1358-1366 and the active EM backend over appendix.tex:1358-1387.",
    "The supplied hypothesis being reduced is exactly hlog : Admissible logRatioTest, not raw KL differentiability or weak FP.",
    "Cycle 87 finite-KL llr regularity is used as a dependency; AC/measurability/integrability should not be reintroduced as separate supplied hypotheses.",
    "The missing theorem names smoothing/Sobolev approximation, boundary behavior, weak-FP action closure, density/time regularity, and zero-set convention.",
    "No theorem status, EM/KL 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.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryLowerObligation",
      "SALD.generalMovingTargetDiscreteKlLogRatioLlrDef",
      "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
      "SALD.GeneralMovingTargetDiscreteKlLogRatioAdmissibilityClosure",
      "SALD.generalMovingTargetDiscreteKlLogRatioAdmissibleOfFiniteKlClosure",
      "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfRawKlAndSourceSignsWithLogAction",
      "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "eq:general_KL_derivative_0_discrete",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  status := ProofStatus.obligation

/-- Cycle-88 middle source map for the log-ratio admissibility boundary. -/