AutoSamplingTheory.SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperPacket

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 cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperPacket :
    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 82 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 the KL-derivative handoff from the cycle-82 endpoint/conditional weak-FP source signs, still inside 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. eq:general_KL_derivative_0_discrete
2. proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp
3. proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative
4. sald.general_moving_target_discrete.em_interpolation_fp
5. sald.general_moving_target_discrete.kl_derivative
6. sald.general_moving_target_discrete.cycle83_kl_derivative_endpoint_weak_fp_upper
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. Cycle 82 supplies only a local endpoint/conditional wrapper for the weak-test source signs; it does not prove the analytic weak Fokker-Planck theorem.
2. Cycle 83 starts at appendix.tex:1358-1366, the differentiated KL display dK=partialS(logRatioTest)-targetTimeTerm after the mass-conservation drop.
3. The active weak-FP input is appendix.tex:1379-1387 with source signs partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi.
4. The new local wrapper composes SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff with SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns.
5. The lower companion SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction keeps the log-ratio weak-FP action and the dK display paired under the same admissibility hypothesis.
6. Gronwall, DV, LSI/KL/FI, continuous KL derivative, density/AC, log-ratio admissibility, integration by parts, FI identification, theorem closure, SLT reuse, and Lake dependencies remain below formalized.

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 with s in [s_k,s_{k+1}] inside appendix.tex:1358-1387.
2. 2. Use cycle-81/cycle-82 endpoint and conditional-readiness hypotheses only to obtain the normalized weak-FP source signs.
3. 3. Select phi_s=log(hat rho_s/tilde pi_s) by an explicit admissibility hypothesis.
4. 4. Substitute the source-signed weak-FP identity into eq:general_KL_derivative_0_discrete, preserving the negative drift-divergence action, positive sigma_eta^2/2 Laplacian action, and unchanged target-time term.
5. 5. Hand the resulting display to sald.general_moving_target_discrete.kl_derivative before later integration by parts, Laplacian split, FI, LSI, DV, time-change, and Gronwall 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:1358-1387 and keep sald_version_2.tex out of scope.
2. Do not change theorem statements, constants, sigma_eta^2/2 sign conventions, source labels, or proof order.
3. Keep conditional law, density/time regularity, generator-to-law calculus, weak FP, KL differentiation, log-ratio admissibility, and boundary assumptions explicit as obligations.

nonGoals : List String (explicit)

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

Ordered data items

1. No theorem-route audit, source-index rebaseline beyond the gate, display algebra outside the KL handoff, frozen-delta work, Gronwall/DV/LSI work, broad reusable API design, or project-article export.
2. No proof of the regular conditional law, density/absolute-continuity, weak Fokker-Planck theorem, KL differentiability theorem, integration-by-parts theorem, or Fisher-information identity.
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.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff / SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation / sald.general_moving_target_discrete.cycle83_kl_derivative_endpoint_weak_fp_lower.
2. Middle should synchronize the source-to-Lean route from cycle-82 endpoint source signs to eq:general_KL_derivative_0_discrete, with the log-ratio admissibility hypothesis explicit.
3. Lower proof-producing scope is only the local composition from endpoint/conditional weak-FP source signs to the KL derivative display; all analytic hypotheses stay supplied.
4. If blocked, record the exact missing Mathlib/SDE theorem boundary rather than broadening to unrelated theorem routes.

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 KL handoff preserves source signs: negative drift-divergence and positive sigma_eta^2/2 Laplacian coefficient.
3. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff is a local composition wrapper and does not prove weak FP, conditional law, density/AC, KL differentiation, integration by parts, FI, LSI, DV, Gronwall, or theorem closure.
4. Both discrete theorem contracts remain contractOnly; analytic backend, SLT, and Lake statuses remain unpromoted.
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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation
2. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation
3. SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation
4. SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction
7. SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff
8. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
9. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation
10. SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation
11. sald.general_moving_target_discrete.em_interpolation_fp
12. sald.general_moving_target_discrete.kl_derivative
13. 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 cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Global phase judgment: cycle 82 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 the KL-derivative handoff from the cycle-82 endpoint/conditional weak-FP source signs, still inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387."
  sourceLabels := [
    "eq:general_KL_derivative_0_discrete",
    "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.cycle83_kl_derivative_endpoint_weak_fp_upper",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Cycle 82 supplies only a local endpoint/conditional wrapper for the weak-test source signs; it does not prove the analytic weak Fokker-Planck theorem.",
    "Cycle 83 starts at appendix.tex:1358-1366, the differentiated KL display dK=partialS(logRatioTest)-targetTimeTerm after the mass-conservation drop.",
    "The active weak-FP input is appendix.tex:1379-1387 with source signs partialS phi = -(driftDiv phi) + (sigma_eta^2/2)*laplacian phi.",
    "The new local wrapper composes SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff with SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns.",
    "The lower companion SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction keeps the log-ratio weak-FP action and the dK display paired under the same admissibility hypothesis.",
    "Gronwall, DV, LSI/KL/FI, continuous KL derivative, density/AC, log-ratio admissibility, integration by parts, FI identification, theorem closure, SLT reuse, and Lake dependencies remain below formalized."
  ]
  theoremRoute := [
    "1. Stay on a fixed EM interval k with s in [s_k,s_{k+1}] inside appendix.tex:1358-1387.",
    "2. Use cycle-81/cycle-82 endpoint and conditional-readiness hypotheses only to obtain the normalized weak-FP source signs.",
    "3. Select phi_s=log(hat rho_s/tilde pi_s) by an explicit admissibility hypothesis.",
    "4. Substitute the source-signed weak-FP identity into eq:general_KL_derivative_0_discrete, preserving the negative drift-divergence action, positive sigma_eta^2/2 Laplacian action, and unchanged target-time term.",
    "5. Hand the resulting display to sald.general_moving_target_discrete.kl_derivative before later integration by parts, Laplacian split, FI, LSI, DV, time-change, and Gronwall obligations."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: preserve appendix.tex:1358-1387 and keep sald_version_2.tex out of scope.",
    "Do not change theorem statements, constants, sigma_eta^2/2 sign conventions, source labels, or proof order.",
    "Keep conditional law, density/time regularity, generator-to-law calculus, weak FP, KL differentiation, log-ratio admissibility, and boundary assumptions explicit as obligations."
  ]
  nonGoals := [
    "No theorem-route audit, source-index rebaseline beyond the gate, display algebra outside the KL handoff, frozen-delta work, Gronwall/DV/LSI work, broad reusable API design, or project-article export.",
    "No proof of the regular conditional law, density/absolute-continuity, weak Fokker-Planck theorem, KL differentiability theorem, integration-by-parts theorem, or Fisher-information identity.",
    "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.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff / SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation / sald.general_moving_target_discrete.cycle83_kl_derivative_endpoint_weak_fp_lower.",
    "Middle should synchronize the source-to-Lean route from cycle-82 endpoint source signs to eq:general_KL_derivative_0_discrete, with the log-ratio admissibility hypothesis explicit.",
    "Lower proof-producing scope is only the local composition from endpoint/conditional weak-FP source signs to the KL derivative display; all analytic hypotheses stay supplied.",
    "If blocked, record the exact missing Mathlib/SDE theorem boundary rather than broadening to unrelated theorem routes."
  ]
  reviewerChecklist := [
    "The active packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.",
    "The KL handoff preserves source signs: negative drift-divergence and positive sigma_eta^2/2 Laplacian coefficient.",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff is a local composition wrapper and does not prove weak FP, conditional law, density/AC, KL differentiation, integration by parts, FI, LSI, DV, Gronwall, or theorem closure.",
    "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.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsUpperObligation",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsMiddleObligation",
    "SALD.cycle82GeneralMovingTargetDiscreteWeakFpSourceSignsLowerObligation",
    "SALD.generalMovingTargetDiscreteEndpointConditionalWeakFpSourceSignsHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSignsWithLogAction",
    "SALD.generalMovingTargetDiscreteEndpointConditionalKlDerivativeWeakFpHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpMiddleObligation",
    "SALD.cycle83GeneralMovingTargetDiscreteKlDerivativeEndpointWeakFpLowerObligation",
    "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-83 upper obligation selecting the endpoint weak-FP to KL handoff. -/