AutoSamplingTheory.SALD.cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperPacket

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 cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperPacket :
    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.

Global phase judgment: cycle 86 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 KL/log-ratio analytic boundary at appendix.tex:1358-1366. Lower should formalize or sharply isolate KL differentiability at the admissible log-ratio weak test, including log-ratio measurability/integrability and the handoff from weak-FP action to dK, without changing theorem statements.

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.cycle87_kl_log_ratio_boundary_upper
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
7. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
8. thm:forward-KL-discrete
9. 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:1358-1366.
2. Cycle 83 and cycle 84 already record supplied-hypothesis handoffs from weak-FP source signs at the log-ratio test to the dK display; lower must not add another handoff of the same shape.
3. Cycle 86 narrows the upstream weak-FP generator boundary, so cycle 87 should attack the remaining KL-side supplied hypotheses: the differentiated KL identity, admissibility of log(hat rho_s / tilde pi_s) as a weak test, log-ratio measurability/integrability, and the mass-conservation term integral partial_s hat rho_s dx = 0.
4. The cycle-87 lower log-ratio regularity theorem discharges the separate absolute-continuity, measurability, and integrability side of the Mathlib llr weak test from the smaller finite-KL hypothesis, while weak-test admissibility and KL differentiability remain obligations.
5. If the full KL derivative theorem is too large, lower should record the smallest named theorem boundary, such as differentiating KL under the integral, finite log-ratio action against partial_s hat rho_s, target-density time-derivative integrability, or admissible weak-test regularity.
6. Accepted progress is discharges-supplied-hypothesis only if an older hkl, hlog, log-action, measurability, or integrability supplied hypothesis is removed; otherwise it must be narrows-source-cited-boundary with a strictly smaller missing theorem.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. Preserve appendix.tex:1358-1366: d/ds KL(hat rho_s || tilde pi_s) equals the partial_s hat rho_s log-ratio action minus the target-time term, using integral partial_s hat rho_s dx = 0.
2. 2. Work before the existing cycle-83/cycle-84 weak-FP-to-KL wrappers by proving or narrowing the KL derivative display and admissible log-ratio weak-test conditions.
3. 3. Feed the resulting log-ratio test and dK display into the existing source-sign handoffs only after the KL/log-ratio hypotheses have been reduced.
4. 4. Keep integration by parts, Fisher-information identification, LSI, DV, Gronwall, frozen-delta work, 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 appendix.tex:1358-1366, eq:general_KL_derivative_0_discrete, the target-time term sign, and both discrete theorem statements.
2. Do not add KL differentiability, density, absolute-continuity, admissible-test, or integrability assumptions to thm:forward-KL-discrete or thm:general-moving-target-SALD-discrete; such hypotheses belong only inside 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 outside appendix.tex:1358-1366, Gronwall/DV/LSI/frozen-delta work, conditional-law work, generator-to-law weak-FP work, reusable API redesign, or project-article export.
2. No new supplied-hypothesis wrapper unless it removes an older KL/log-ratio supplied hypothesis, exposes a strictly smaller missing theorem, or compiles a genuinely local proof.
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 sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to the KL/log-ratio analytic boundary at appendix.tex:1358-1366.
2. Preferred product: a compiled local theorem that removes an older supplied hkl-style KL derivative display, hlog-style log-ratio admissibility hypothesis, or log-ratio measurability/integrability hypothesis used by the cycle-83/cycle-84 wrappers.
3. Allowed blocked product: one precise source-cited theorem boundary naming the missing Mathlib/local theorem, imports, and hypotheses for KL differentiability under the integral, finite log-ratio weak-FP action, target-density time derivative, mass conservation, or admissible weak-test regularity.
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:1358-1366.
2. Reject any packet that only composes existing cycle-83/cycle-84 hkl/hlog/log-action wrappers without removing an existing supplied hypothesis or naming a smaller missing theorem.
3. Check that eq:general_KL_derivative_0_discrete keeps the target-time term with the paper's minus sign and uses the mass-conservation statement integral partial_s hat rho_s dx = 0.
4. Check that the log-density-ratio weak test has explicit measurability, integrability, density/zero-set, and admissible-test hypotheses, or that the exact missing theorem is named.
5. No theorem status, EM backend status, KL derivative 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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff
3. SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation
4. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
6. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
7. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
8. SALD.generalMovingTargetDiscreteKlLogRatioLlrDef
9. SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl
10. eq:general_KL_derivative_0_discrete
11. proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative
12. Mathlib.InformationTheory.KullbackLeibler.Basic
13. Mathlib.MeasureTheory.Measure.LogLikelihoodRatio
14. Mathlib.MeasureTheory.Integral.Bochner.Basic
15. Mathlib.Analysis.Calculus.ParametricIntegral
16. sald.general_moving_target_discrete.em_interpolation_fp
17. sald.discrete_forward_kl.em_interpolation_fp
18. 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 cycle87GeneralMovingTargetDiscreteKlLogRatioBoundaryUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Global phase judgment: cycle 86 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 KL/log-ratio analytic boundary at appendix.tex:1358-1366. Lower should formalize or sharply isolate KL differentiability at the admissible log-ratio weak test, including log-ratio measurability/integrability and the handoff from weak-FP action to dK, without changing theorem statements."
  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.cycle87_kl_log_ratio_boundary_upper",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
    "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:1358-1366.",
    "Cycle 83 and cycle 84 already record supplied-hypothesis handoffs from weak-FP source signs at the log-ratio test to the dK display; lower must not add another handoff of the same shape.",
    "Cycle 86 narrows the upstream weak-FP generator boundary, so cycle 87 should attack the remaining KL-side supplied hypotheses: the differentiated KL identity, admissibility of log(hat rho_s / tilde pi_s) as a weak test, log-ratio measurability/integrability, and the mass-conservation term integral partial_s hat rho_s dx = 0.",
    "The cycle-87 lower log-ratio regularity theorem discharges the separate absolute-continuity, measurability, and integrability side of the Mathlib llr weak test from the smaller finite-KL hypothesis, while weak-test admissibility and KL differentiability remain obligations.",
    "If the full KL derivative theorem is too large, lower should record the smallest named theorem boundary, such as differentiating KL under the integral, finite log-ratio action against partial_s hat rho_s, target-density time-derivative integrability, or admissible weak-test regularity.",
    "Accepted progress is discharges-supplied-hypothesis only if an older hkl, hlog, log-action, measurability, or integrability supplied hypothesis is removed; otherwise it must be narrows-source-cited-boundary with a strictly smaller missing theorem."
  ]
  theoremRoute := [
    "1. Preserve appendix.tex:1358-1366: d/ds KL(hat rho_s || tilde pi_s) equals the partial_s hat rho_s log-ratio action minus the target-time term, using integral partial_s hat rho_s dx = 0.",
    "2. Work before the existing cycle-83/cycle-84 weak-FP-to-KL wrappers by proving or narrowing the KL derivative display and admissible log-ratio weak-test conditions.",
    "3. Feed the resulting log-ratio test and dK display into the existing source-sign handoffs only after the KL/log-ratio hypotheses have been reduced.",
    "4. Keep integration by parts, Fisher-information identification, LSI, DV, Gronwall, frozen-delta work, and theorem closure as downstream consumers."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: preserve appendix.tex:1358-1366, eq:general_KL_derivative_0_discrete, the target-time term sign, and both discrete theorem statements.",
    "Do not add KL differentiability, density, absolute-continuity, admissible-test, or integrability assumptions to thm:forward-KL-discrete or thm:general-moving-target-SALD-discrete; such hypotheses belong only inside 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 outside appendix.tex:1358-1366, Gronwall/DV/LSI/frozen-delta work, conditional-law work, generator-to-law weak-FP work, reusable API redesign, or project-article export.",
    "No new supplied-hypothesis wrapper unless it removes an older KL/log-ratio supplied hypothesis, exposes a strictly smaller missing theorem, or compiles a genuinely local proof.",
    "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 sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to the KL/log-ratio analytic boundary at appendix.tex:1358-1366.",
    "Preferred product: a compiled local theorem that removes an older supplied hkl-style KL derivative display, hlog-style log-ratio admissibility hypothesis, or log-ratio measurability/integrability hypothesis used by the cycle-83/cycle-84 wrappers.",
    "Allowed blocked product: one precise source-cited theorem boundary naming the missing Mathlib/local theorem, imports, and hypotheses for KL differentiability under the integral, finite log-ratio weak-FP action, target-density time derivative, mass conservation, or admissible weak-test regularity.",
    "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:1358-1366.",
    "Reject any packet that only composes existing cycle-83/cycle-84 hkl/hlog/log-action wrappers without removing an existing supplied hypothesis or naming a smaller missing theorem.",
    "Check that eq:general_KL_derivative_0_discrete keeps the target-time term with the paper's minus sign and uses the mass-conservation statement integral partial_s hat rho_s dx = 0.",
    "Check that the log-density-ratio weak test has explicit measurability, integrability, density/zero-set, and admissible-test hypotheses, or that the exact missing theorem is named.",
    "No theorem status, EM backend status, KL derivative 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.cycle86GeneralMovingTargetDiscreteWeakFpGeneratorBoundaryLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleGeneratorPiecesHandoff",
    "SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendLowerObligation",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
    "SALD.generalMovingTargetDiscreteKlLogRatioLlrDef",
    "SALD.generalMovingTargetDiscreteKlLogRatioRegularityOfFiniteKl",
    "eq:general_KL_derivative_0_discrete",
    "proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative",
    "Mathlib.InformationTheory.KullbackLeibler.Basic",
    "Mathlib.MeasureTheory.Measure.LogLikelihoodRatio",
    "Mathlib.MeasureTheory.Integral.Bochner.Basic",
    "Mathlib.Analysis.Calculus.ParametricIntegral",
    "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-87 upper obligation selecting the KL/log-ratio analytic boundary. -/