AutoSamplingTheory.SALD.cycle74GeneralMovingTargetDiscreteMeasureInterfaceUpperPacket

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 cycle74GeneralMovingTargetDiscreteMeasureInterfaceUpperPacket :
    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 73 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; proof-producing work on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 is now blocked on the concrete conditional-law measure backend, so the single lower packet is the narrow Mathlib condExpKernel/conditional-kernel interface for appendix.tex:1368-1377.

sourceLabels : List String (explicit)

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

Ordered data items

1. proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative
2. proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp
3. sald.general_moving_target_discrete.em_interpolation_fp
4. sald.general_moving_target_discrete.cycle74_conditional_kernel_measure_interface
5. thm:forward-KL-discrete
6. 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, DV, LSI/KL/FI, and continuous Fokker-Planck/KL derivative interfaces are unchanged and remain below formalized status.
2. Cycles 70-73 already provide local wrappers for named conditional drift, endpoint-to-conditional compatibility, weak-FP source signs, and weak-FP-to-KL scalar substitution under explicit hypotheses.
3. The remaining blocked interface is the regular conditional-kernel/conditional-expectation measure theorem feeding bar b_{k,s}; cycle 74 records it as sourceCited through Mathlib Probability.Kernel.Condexp rather than pretending the analytic backend is formalized.
4. The weak conditional Fokker-Planck theorem, log-ratio admissibility, density/AC, integration by parts, and KL differentiation remain obligations after this cited interface.

theoremRoute : List String (explicit)

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

Ordered data items

1. 1. Stay inside appendix.tex:1358-1387 and the existing sald.general_moving_target_discrete.em_interpolation_fp backend.
2. 2. Use appendix.tex:1368-1377 as the selected source slice: construct/name the conditional law of X_k^eta given hat X_s=x and the conditional drift bar b_{k,s}.
3. 3. Cite the Mathlib condExpKernel/condDistrib measure interface as the missing theorem to audit, with standard-Borel, finite/probability, measurability, integrability, marginal-compatibility, and kernel-version side conditions explicit.
4. 4. Do not advance to new theorem-route audits or unrelated scalar algebra until this conditional-law interface is either locally proved or kept as a precise cited dependency.

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1: preserve the original appendix.tex source route and exclude sald_version_2.tex.
2. Do not add assumptions to thm:forward-KL-discrete or thm:general-moving-target-SALD-discrete; record required standard-Borel, finite-measure, measurability, and integrability side conditions as interface obligations.
3. Keep every cited or analytic backend below formalized unless the local ASTIS declaration compiles under this toolchain.

nonGoals : List String (explicit)

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

Ordered data items

1. No broad SLT import, no Lake dependency change, and no claim that any SLT theorem is formalized.
2. No theorem-route audit, Gronwall/DV/LSI display work, frozen-delta algebra, or project-article export.
3. No promotion of the weak conditional Fokker-Planck theorem, KL derivative backend, EM interpolation backend, or theorem contracts.

lowerPacket : List String (explicit)

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

Ordered data items

1. Target exactly SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface / sald.general_moving_target_discrete.cycle74_conditional_kernel_measure_interface.
2. Middle should synchronize the paper-to-Lean map for appendix.tex:1368-1377 and the Mathlib candidates Probability.Kernel.Condexp, CondDistrib, and Disintegration.StandardBorel.
3. Lower should either prove a tiny local wrapper around the conditional-kernel interface under explicit supplied hypotheses, or leave this exact sourceCited interface as the blocker; do not switch to weak FP, KL derivative, theorem-route, or display algebra work.

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, narrowed to appendix.tex:1368-1377.
2. The new measure interface is ProofStatus.sourceCited, not formalized, and no Mathlib/SLT theorem is claimed imported or locally proved.
3. discrete and discrete-general theorem contracts remain ProofStatus.contractOnly and list the cycle-74 interface only as a dependency.
4. The conversion window, proof-obligation ledger, and SLT reuse audit record the same conditional-kernel blocker.
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.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation
2. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
3. SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract
4. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
5. SALD.generalMovingTargetDiscreteConditionalDriftContract
6. sald.general_moving_target_discrete.em_interpolation_fp
7. Mathlib.Probability.Kernel.Condexp

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 cycle74GeneralMovingTargetDiscreteMeasureInterfaceUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Global phase judgment: cycle 73 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; proof-producing work on sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387 is now blocked on the concrete conditional-law measure backend, so the single lower packet is the narrow Mathlib condExpKernel/conditional-kernel interface for appendix.tex:1368-1377."
  sourceLabels := [
    "proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative",
    "proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.cycle74_conditional_kernel_measure_interface",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "Gronwall, DV, LSI/KL/FI, and continuous Fokker-Planck/KL derivative interfaces are unchanged and remain below formalized status.",
    "Cycles 70-73 already provide local wrappers for named conditional drift, endpoint-to-conditional compatibility, weak-FP source signs, and weak-FP-to-KL scalar substitution under explicit hypotheses.",
    "The remaining blocked interface is the regular conditional-kernel/conditional-expectation measure theorem feeding bar b_{k,s}; cycle 74 records it as sourceCited through Mathlib Probability.Kernel.Condexp rather than pretending the analytic backend is formalized.",
    "The weak conditional Fokker-Planck theorem, log-ratio admissibility, density/AC, integration by parts, and KL differentiation remain obligations after this cited interface."
  ]
  theoremRoute := [
    "1. Stay inside appendix.tex:1358-1387 and the existing sald.general_moving_target_discrete.em_interpolation_fp backend.",
    "2. Use appendix.tex:1368-1377 as the selected source slice: construct/name the conditional law of X_k^eta given hat X_s=x and the conditional drift bar b_{k,s}.",
    "3. Cite the Mathlib condExpKernel/condDistrib measure interface as the missing theorem to audit, with standard-Borel, finite/probability, measurability, integrability, marginal-compatibility, and kernel-version side conditions explicit.",
    "4. Do not advance to new theorem-route audits or unrelated scalar algebra until this conditional-law interface is either locally proved or kept as a precise cited dependency."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: preserve the original appendix.tex source route and exclude sald_version_2.tex.",
    "Do not add assumptions to thm:forward-KL-discrete or thm:general-moving-target-SALD-discrete; record required standard-Borel, finite-measure, measurability, and integrability side conditions as interface obligations.",
    "Keep every cited or analytic backend below formalized unless the local ASTIS declaration compiles under this toolchain."
  ]
  nonGoals := [
    "No broad SLT import, no Lake dependency change, and no claim that any SLT theorem is formalized.",
    "No theorem-route audit, Gronwall/DV/LSI display work, frozen-delta algebra, or project-article export.",
    "No promotion of the weak conditional Fokker-Planck theorem, KL derivative backend, EM interpolation backend, or theorem contracts."
  ]
  lowerPacket := [
    "Target exactly SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface / sald.general_moving_target_discrete.cycle74_conditional_kernel_measure_interface.",
    "Middle should synchronize the paper-to-Lean map for appendix.tex:1368-1377 and the Mathlib candidates Probability.Kernel.Condexp, CondDistrib, and Disintegration.StandardBorel.",
    "Lower should either prove a tiny local wrapper around the conditional-kernel interface under explicit supplied hypotheses, or leave this exact sourceCited interface as the blocker; do not switch to weak FP, KL derivative, theorem-route, or display algebra work."
  ]
  reviewerChecklist := [
    "The active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to appendix.tex:1368-1377.",
    "The new measure interface is ProofStatus.sourceCited, not formalized, and no Mathlib/SLT theorem is claimed imported or locally proved.",
    "discrete and discrete-general theorem contracts remain ProofStatus.contractOnly and list the cycle-74 interface only as a dependency.",
    "The conversion window, proof-obligation ledger, and SLT reuse audit record the same conditional-kernel blocker.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle73GeneralMovingTargetDiscreteKlDerivativeWeakFpLowerObligation",
    "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
    "SALD.generalMovingTargetDiscreteConditionalLawMeasurabilityContract",
    "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
    "SALD.generalMovingTargetDiscreteConditionalDriftContract",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "Mathlib.Probability.Kernel.Condexp"
  ]
  status := ProofStatus.obligation

/-- Cycle-74 upper obligation for the minimal cited measure interface. -/