AutoSamplingTheory.SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorUpperPacket

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 cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorUpperPacket :
    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 77 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-77 generator-level weak conditional Fokker-Planck 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. eq:general_KL_derivative_1_discrete
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. 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. Gronwall remains unchanged as endpoint-safe calculus and theorem-specific coefficient/display obligations; cycle 78 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 78 is still before the residual DV step.
3. LSI/KL/FI remains the density-test/Fisher-chain obligation; cycle 78 only prepares the derivative handoff that later feeds the Fisher-information identification.
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 70-77 exposed conditional-law, endpoint compatibility, weak FP signs, KL substitution, conditional-kernel measure interfaces, endpoint-to-conditional packaging, and generator source signs; cycle 78 connects the generator pieces to the log-ratio KL derivative substitution.

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:1379-1387 through the cycle-77 supplied generator/time-derivative, generator split, and drift/diffusion source-action hypotheses.
3. 3. Select phi_s=log(hat rho_s/tilde pi_s) as the weak test only through an explicit admissibility hypothesis.
4. 4. Compose the generator-piece weak FP source signs through the normalized source-sign-to-KL wrapper, preserving the negative drift-divergence action, positive sigma_eta^2/2 Laplacian action, and unchanged target-time term.
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 generator theorem, regular conditional law, log-ratio admissibility, density/absolute-continuity, finite KL/FI, boundary, integration-by-parts, and weak FP 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, LSI/KL/FI proof work, or broad SLT/SDE API backfill.
2. No claim that a regular conditional law, weak Fokker-Planck theorem, generator 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.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces / SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation / sald.general_moving_target_discrete.cycle78_kl_derivative_generator_lower.
2. Lower proof-producing scope: compile only the scalar composition from the differentiated KL formula plus the cycle-77 supplied generator/time-derivative, generator split, drift source action, diffusion source action, and sigmaCoeff=sigma_eta^2/2 hypotheses at the admissible log-ratio test.
3. Middle synchronization scope: update the conversion window and proof-obligation ledger so cycle 77 generator pieces and cycle 73 KL substitution are visible as one ordered source route over 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.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces is a local equality-composition wrapper only and does not prove the generator theorem, weak FP theorem, or KL derivative backend.
3. SALD.discreteSaldContract and SALD.generalVaSaldDiscreteContract remain contractOnly and list the cycle-78 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.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation
2. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff
3. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract
4. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns
5. SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces
6. SALD.generalMovingTargetDiscreteDerivativeSideConditionContract
7. sald.general_moving_target_discrete.em_interpolation_fp
8. 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 cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Global phase judgment: cycle 77 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-77 generator-level weak conditional Fokker-Planck source signs, still inside sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387."
  sourceLabels := [
    "eq:general_KL_derivative_0_discrete",
    "eq:general_KL_derivative_1_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 78 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 78 is still before the residual DV step.",
    "LSI/KL/FI remains the density-test/Fisher-chain obligation; cycle 78 only prepares the derivative handoff that later feeds the Fisher-information identification.",
    "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 70-77 exposed conditional-law, endpoint compatibility, weak FP signs, KL substitution, conditional-kernel measure interfaces, endpoint-to-conditional packaging, and generator source signs; cycle 78 connects the generator pieces to the log-ratio KL derivative substitution."
  ]
  theoremRoute := [
    "1. Start from appendix.tex:1358-1366, the differentiated KL display and mass-conservation drop.",
    "2. Use appendix.tex:1379-1387 through the cycle-77 supplied generator/time-derivative, generator split, and drift/diffusion source-action hypotheses.",
    "3. Select phi_s=log(hat rho_s/tilde pi_s) as the weak test only through an explicit admissibility hypothesis.",
    "4. Compose the generator-piece weak FP source signs through the normalized source-sign-to-KL wrapper, preserving the negative drift-divergence action, positive sigma_eta^2/2 Laplacian action, and unchanged target-time term.",
    "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 generator theorem, regular conditional law, log-ratio admissibility, density/absolute-continuity, finite KL/FI, boundary, integration-by-parts, and weak FP assumptions as explicit obligations, not hidden theorem hypotheses."
  ]
  nonGoals := [
    "No theorem-route audit, display algebra, Gronwall coefficient work, DV witness work, LSI/KL/FI proof work, or broad SLT/SDE API backfill.",
    "No claim that a regular conditional law, weak Fokker-Planck theorem, generator 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.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces / SALD.cycle78GeneralMovingTargetDiscreteKlDerivativeGeneratorLowerObligation / sald.general_moving_target_discrete.cycle78_kl_derivative_generator_lower.",
    "Lower proof-producing scope: compile only the scalar composition from the differentiated KL formula plus the cycle-77 supplied generator/time-derivative, generator split, drift source action, diffusion source action, and sigmaCoeff=sigma_eta^2/2 hypotheses at the admissible log-ratio test.",
    "Middle synchronization scope: update the conversion window and proof-obligation ledger so cycle 77 generator pieces and cycle 73 KL substitution are visible as one ordered source route over 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.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces is a local equality-composition wrapper only and does not prove the generator theorem, weak FP theorem, or KL derivative backend.",
    "SALD.discreteSaldContract and SALD.generalVaSaldDiscreteContract remain contractOnly and list the cycle-78 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.cycle77GeneralMovingTargetDiscreteWeakFpGeneratorLowerObligation",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfGeneratorPiecesHandoff",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffContract",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfSourceSigns",
    "SALD.generalMovingTargetDiscreteKlDerivativeWeakFpHandoffOfGeneratorPieces",
    "SALD.generalMovingTargetDiscreteDerivativeSideConditionContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative"
  ]
  status := ProofStatus.obligation

/-- Cycle-78 upper obligation for the generator-to-KL handoff packet. -/