AutoSamplingTheory.SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpUpperPacket

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 cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpUpperPacket :
    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 72 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for continued single-backend cited-theory backfill; the single lower packet that best reduces the remaining proof risk is the KL-derivative handoff from the weak conditional Fokker-Planck identity, 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. thm:forward-KL-discrete
7. 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. Gronwall remains unchanged as endpoint-safe calculus and theorem-specific coefficient/display obligations; cycle 73 does not touch lem:gronwall.
2. DV remains source-cited through lem:dv_variation with common-space, absolute-continuity, finite-KL, and finite-log-mgf witnesses; cycle 73 is before the residual DV step.
3. LSI/KL/FI remains the density-test/Fisher-chain obligation; cycle 73 does not use eq:LSI-KL-FI except as a downstream derivative consumer.
4. Continuous Fokker-Planck/KL derivative remains a separate continuous theorem backend and is not modified by this EM packet.
5. EM interpolation FP remains the active backend: cycles 70-72 exposed conditional-law, endpoint compatibility, and weak FP signs; cycle 73 now exposes the log-ratio-test substitution into the differentiated KL formula.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. Start from appendix.tex:1358-1366, the differentiated KL display and mass-conservation drop.
2. 2. Use appendix.tex:1368-1377 only through the already named conditional drift and conditional-kernel interfaces.
3. 3. Use appendix.tex:1379-1387 through the supplied weak conditional FP identity with the cycle-72 source signs.
4. 4. Substitute that weak FP identity at the log-density-ratio test and hand the result to sald.general_moving_target_discrete.kl_derivative.
5. 5. Leave integration by parts, Laplacian split, FI identification, LSI, DV, time change, Gronwall, and theorem closure as separate obligations.

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1: use only the original appendix.tex source window 1358-1387; sald_version_2.tex remains excluded.
2. Do not change theorem statements, constants, sigma_eta^2/2 sign conventions, source labels, or proof order.
3. Keep the log-ratio admissibility, density/absolute-continuity, finite KL/FI, boundary, integration-by-parts, and weak FP theorem assumptions as explicit obligations, not hidden theorem hypotheses.

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 coefficient work, DV witness work, or broad SLT/SDE API backfill.
2. No claim that a regular conditional law, weak Fokker-Planck theorem, log-ratio admissibility theorem, or KL differentiation theorem is formalized.
3. No promotion of thm:forward-KL-discrete, thm:general-moving-target-SALD-discrete, LSI/KL/FI, DV, Gronwall, or EM interpolation status.

lowerPacket : List String (explicit)

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

Ordered data items

1. Target exactly SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract / SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation / sald.general_moving_target_discrete.cycle73_kl_derivative_weak_fp_lower.
2. Lower proof-producing scope: compile only the scalar substitution from the differentiated KL formula plus the supplied admissible weak FP identity at the log-ratio test, including the direct composition through the cycle-72 admissible source-sign wrapper.
3. Middle synchronization scope: keep the source-to-Lean map two-way synchronized in the conversion window, proof-obligation ledger, and SLT audit under appendix.tex:1358-1387.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. The active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.
2. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns are local substitution wrappers only and do not prove the analytic weak FP or KL derivative backend.
3. SALD.discreteSaldContract and SALD.generalVaSaldDiscreteContract remain contractOnly and list the cycle-73 obligations.
4. Gronwall, DV, LSI/KL/FI, continuous FP/KL derivative, EM interpolation, theorem statuses, and SLT reuse statuses remain below formalized.
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.cycle72GeneralMovingTargetDiscreteWeakFpMiddleObligation
2. SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation
3. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract
4. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
6. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar
7. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns
8. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
9. sald.general_moving_target_discrete.em_interpolation_fp
10. 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 cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Global phase judgment: cycle 72 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for continued single-backend cited-theory backfill; the single lower packet that best reduces the remaining proof risk is the KL-derivative handoff from the weak conditional Fokker-Planck identity, 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",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Gronwall remains unchanged as endpoint-safe calculus and theorem-specific coefficient/display obligations; cycle 73 does not touch lem:gronwall.",
    "DV remains source-cited through lem:dv_variation with common-space, absolute-continuity, finite-KL, and finite-log-mgf witnesses; cycle 73 is before the residual DV step.",
    "LSI/KL/FI remains the density-test/Fisher-chain obligation; cycle 73 does not use eq:LSI-KL-FI except as a downstream derivative consumer.",
    "Continuous Fokker-Planck/KL derivative remains a separate continuous theorem backend and is not modified by this EM packet.",
    "EM interpolation FP remains the active backend: cycles 70-72 exposed conditional-law, endpoint compatibility, and weak FP signs; cycle 73 now exposes the log-ratio-test substitution into the differentiated KL formula."
  ]
  theoremRoute := [
    "1. Start from appendix.tex:1358-1366, the differentiated KL display and mass-conservation drop.",
    "2. Use appendix.tex:1368-1377 only through the already named conditional drift and conditional-kernel interfaces.",
    "3. Use appendix.tex:1379-1387 through the supplied weak conditional FP identity with the cycle-72 source signs.",
    "4. Substitute that weak FP identity at the log-density-ratio test and hand the result to sald.general_moving_target_discrete.kl_derivative.",
    "5. Leave integration by parts, Laplacian split, FI identification, LSI, DV, time change, Gronwall, and theorem closure as separate obligations."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: use only the original appendix.tex source window 1358-1387; sald_version_2.tex remains excluded.",
    "Do not change theorem statements, constants, sigma_eta^2/2 sign conventions, source labels, or proof order.",
    "Keep the log-ratio admissibility, density/absolute-continuity, finite KL/FI, boundary, integration-by-parts, and weak FP theorem assumptions as explicit obligations, not hidden theorem hypotheses."
  ]
  nonGoals := [
    "No theorem-route audit, display algebra, Gronwall coefficient work, DV witness work, or broad SLT/SDE API backfill.",
    "No claim that a regular conditional law, weak Fokker-Planck theorem, log-ratio admissibility theorem, or KL differentiation theorem is formalized.",
    "No promotion of thm:forward-KL-discrete, thm:general-moving-target-SALD-discrete, LSI/KL/FI, DV, Gronwall, or EM interpolation status."
  ]
  lowerPacket := [
    "Target exactly SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract / SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation / sald.general_moving_target_discrete.cycle73_kl_derivative_weak_fp_lower.",
    "Lower proof-producing scope: compile only the scalar substitution from the differentiated KL formula plus the supplied admissible weak FP identity at the log-ratio test, including the direct composition through the cycle-72 admissible source-sign wrapper.",
    "Middle synchronization scope: keep the source-to-Lean map two-way synchronized in the conversion window, proof-obligation ledger, and SLT audit under appendix.tex:1358-1387."
  ]
  reviewerChecklist := [
    "The active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar and SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns are local substitution wrappers only and do not prove the analytic weak FP or KL derivative backend.",
    "SALD.discreteSaldContract and SALD.generalVaSaldDiscreteContract remain contractOnly and list the cycle-73 obligations.",
    "Gronwall, DV, LSI/KL/FI, continuous FP/KL derivative, EM interpolation, theorem statuses, and SLT reuse statuses remain below formalized.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle72GeneralMovingTargetDiscreteWeakFpMiddleObligation",
    "SALD.cycle72GeneralMovingTargetDiscreteWeakFpLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignContract",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsAdmissibleHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffScalar",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfAdmissibleSourceSigns",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  status := ProofStatus.obligation

/-- Cycle-73 upper obligation for the KL-derivative handoff packet. -/