AutoSamplingTheory.SALD.cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperPacket

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 cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperPacket :
    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 83 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 to keep proving the active sald.general_moving_target_discrete.em_interpolation_fp backend over appendix.tex:1358-1387 by consolidating the cycle-80 to cycle-83 endpoint/conditional readiness, weak-FP source signs, and KL-derivative handoff. The minimal cited Mathlib/measure interface is an escape hatch only if this proof-producing work hits a concrete conditional-law or weak-FP theorem blocker.

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:conditional-drift
3. proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp
4. proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative
5. sald.general_moving_target_discrete.em_interpolation_fp
6. sald.general_moving_target_discrete.kl_derivative
7. sald.general_moving_target_discrete.cycle84_active_em_backend_upper
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. Cycles 80 and 81 expose endpoint/conditional readiness for the named law hat rho_s, conditional kernel, and measurable/integrable bar b_{k,s}.
2. Cycle 82 exposes the weak-test source signs partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi under supplied density, test, boundary, and generator hypotheses.
3. Cycle 83 exposes the admissible log-ratio substitution into eq:general_KL_derivative_0_discrete and pairs the weak-FP action with the resulting dK display.
4. Cycle 84 lower should first try to package these accepted handoffs into the next active EM-backend proof step, not introduce a new broad Mathlib measure interface.
5. If lower is blocked, the only acceptable fallback is one narrow source-cited interface naming the missing conditional-law or generator-to-law weak-FP theorem with common-space, density/AC, admissible-test, finite-integral, and boundary hypotheses explicit.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. Stay on a fixed EM interval k and s in [s_k,s_{k+1}] inside appendix.tex:1358-1387.
2. 2. Start from the cycle-81 endpoint/conditional WeakFpPrereq readiness and the cycle-82 endpoint weak-FP source-sign handoff.
3. 3. Reuse the cycle-83 log-ratio action plus dK display at eq:general_KL_derivative_0_discrete.
4. 4. Select a proof-producing local bridge that makes the EM interpolation FP backend lower-ready for the next KL derivative step while keeping conditional law, density/AC, weak FP, KL differentiability, integration by parts, FI, LSI, DV, and Gronwall explicit.
5. 5. Only if that bridge is blocked, record exactly one cited measure-theory theorem boundary; do not broaden to theorem-route audits, display algebra, or unrelated analytic backends.

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:1358-1387, source labels, signs, constants, and theorem statements; sald_version_2.tex remains out of scope.
2. The minimal measure-interface fallback must not add assumptions to thm:forward-KL-discrete or thm:general-moving-target-SALD-discrete.
3. Use lean-stat-learning-theory only as a local style reference for Mathlib measure/probability patterns; do not import it, change Lake dependencies, or mark any SLT theorem formalized.

nonGoals : List String (explicit)

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

Ordered data items

1. No source-index rebaseline beyond the acceptance gate, broad theorem-route audit, Gronwall/DV/LSI/frozen-delta work, display algebra outside appendix.tex:1358-1387, reusable API redesign, or project-article export.
2. No proof of the full regular conditional law, density/absolute-continuity theorem, generator-to-law weak Fokker-Planck theorem, KL differentiability theorem, integration-by-parts theorem, or theorem closure unless a local declaration actually compiles.
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.
2. Preferred lower work is a proof-producing local bridge that consumes the cycle-81 endpoint/conditional readiness, cycle-82 endpoint source signs, and cycle-83 log-ratio KL handoff to make the EM backend handoff tighter for both discrete theorem routes.
3. Do not introduce a new cited Mathlib/measure interface unless lower can name the precise blocked theorem, whether conditional-law/measurability or generator-to-law weak FP, and lists the exact hypotheses consumed by the source proof.
4. If blocked, the fallback interface must remain sourceCited or obligation-level and must not claim regular conditional law, weak FP, KL derivative, theorem closure, SLT, or Lake status as formalized.

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.
2. The packet does not trigger the measure-interface fallback unless a concrete proof-producing attempt is blocked.
3. Any fallback interface is narrow: one missing conditional-law or weak-FP theorem boundary with common-space, density/AC, admissible-test, finite-integral, boundary, and coefficient hypotheses explicit.
4. The source signs stay negative for drift-divergence and positive for the sigma_eta^2/2 Laplacian coefficient.
5. Both discrete theorem contracts remain contractOnly; analytic backend, SLT, and Lake statuses remain unpromoted.
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.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation
2. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation
3. SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation
4. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
5. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation
6. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation
7. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
8. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff
9. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
10. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff
11. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction
12. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
13. SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface
14. sald.general_moving_target_discrete.em_interpolation_fp
15. sald.general_moving_target_discrete.kl_derivative
16. 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 cycle84GeneralMovingTargetDiscreteActiveEmBackendUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Global phase judgment: cycle 83 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 to keep proving the active sald.general_moving_target_discrete.em_interpolation_fp backend over appendix.tex:1358-1387 by consolidating the cycle-80 to cycle-83 endpoint/conditional readiness, weak-FP source signs, and KL-derivative handoff. The minimal cited Mathlib/measure interface is an escape hatch only if this proof-producing work hits a concrete conditional-law or weak-FP theorem blocker."
  sourceLabels := [
    "eq:general_KL_derivative_0_discrete",
    "proof:thm:general-moving-target-SALD-discrete:conditional-drift",
    "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.kl_derivative",
    "sald.general_moving_target_discrete.cycle84_active_em_backend_upper",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Cycles 80 and 81 expose endpoint/conditional readiness for the named law hat rho_s, conditional kernel, and measurable/integrable bar b_{k,s}.",
    "Cycle 82 exposes the weak-test source signs partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi under supplied density, test, boundary, and generator hypotheses.",
    "Cycle 83 exposes the admissible log-ratio substitution into eq:general_KL_derivative_0_discrete and pairs the weak-FP action with the resulting dK display.",
    "Cycle 84 lower should first try to package these accepted handoffs into the next active EM-backend proof step, not introduce a new broad Mathlib measure interface.",
    "If lower is blocked, the only acceptable fallback is one narrow source-cited interface naming the missing conditional-law or generator-to-law weak-FP theorem with common-space, density/AC, admissible-test, finite-integral, and boundary hypotheses explicit."
  ]
  theoremRoute := [
    "1. Stay on a fixed EM interval k and s in [s_k,s_{k+1}] inside appendix.tex:1358-1387.",
    "2. Start from the cycle-81 endpoint/conditional WeakFpPrereq readiness and the cycle-82 endpoint weak-FP source-sign handoff.",
    "3. Reuse the cycle-83 log-ratio action plus dK display at eq:general_KL_derivative_0_discrete.",
    "4. Select a proof-producing local bridge that makes the EM interpolation FP backend lower-ready for the next KL derivative step while keeping conditional law, density/AC, weak FP, KL differentiability, integration by parts, FI, LSI, DV, and Gronwall explicit.",
    "5. Only if that bridge is blocked, record exactly one cited measure-theory theorem boundary; do not broaden to theorem-route audits, display algebra, or unrelated analytic backends."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: preserve appendix.tex:1358-1387, source labels, signs, constants, and theorem statements; sald_version_2.tex remains out of scope.",
    "The minimal measure-interface fallback must not add assumptions to thm:forward-KL-discrete or thm:general-moving-target-SALD-discrete.",
    "Use lean-stat-learning-theory only as a local style reference for Mathlib measure/probability patterns; do not import it, change Lake dependencies, or mark any SLT theorem formalized."
  ]
  nonGoals := [
    "No source-index rebaseline beyond the acceptance gate, broad theorem-route audit, Gronwall/DV/LSI/frozen-delta work, display algebra outside appendix.tex:1358-1387, reusable API redesign, or project-article export.",
    "No proof of the full regular conditional law, density/absolute-continuity theorem, generator-to-law weak Fokker-Planck theorem, KL differentiability theorem, integration-by-parts theorem, or theorem closure unless a local declaration actually compiles.",
    "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.",
    "Preferred lower work is a proof-producing local bridge that consumes the cycle-81 endpoint/conditional readiness, cycle-82 endpoint source signs, and cycle-83 log-ratio KL handoff to make the EM backend handoff tighter for both discrete theorem routes.",
    "Do not introduce a new cited Mathlib/measure interface unless lower can name the precise blocked theorem, whether conditional-law/measurability or generator-to-law weak FP, and lists the exact hypotheses consumed by the source proof.",
    "If blocked, the fallback interface must remain sourceCited or obligation-level and must not claim regular conditional law, weak FP, KL derivative, theorem closure, SLT, or Lake status as formalized."
  ]
  reviewerChecklist := [
    "The active packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.",
    "The packet does not trigger the measure-interface fallback unless a concrete proof-producing attempt is blocked.",
    "Any fallback interface is narrow: one missing conditional-law or weak-FP theorem boundary with common-space, density/AC, admissible-test, finite-integral, boundary, and coefficient hypotheses explicit.",
    "The source signs stay negative for drift-divergence and positive for the sigma_eta^2/2 Laplacian coefficient.",
    "Both discrete theorem contracts remain contractOnly; analytic backend, SLT, and Lake statuses remain unpromoted.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle80GeneralMovingTargetDiscreteConditionalLawMeasurabilityLowerObligation",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalMiddleObligation",
    "SALD.cycle81GeneralMovingTargetDiscreteEndpointConditionalLowerObligation",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperObligation",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpReadinessHandoff",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoffWithLogAction",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.cycle79GeneralMovingTargetDiscreteWeakFpGeneratorMeasureInterface",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative",
    "sald.discrete_forward_kl.em_interpolation_fp"
  ]
  status := ProofStatus.obligation

/-- Cycle-84 upper obligation selecting active EM-backend proof work before any
minimal cited measure-interface fallback. -/