AutoSamplingTheory.SALD.cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperPacket

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 cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperPacket :
    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 75 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet that now reduces the largest proof risk is endpoint-law-to-conditional-law compatibility for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, especially the bridge from endpoint Measure.map laws to the swapped condDistrib orientation needed by the weak FP interface.

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:conditional-drift
3. proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp
4. sald.general_moving_target_discrete.em_interpolation_fp
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. The endpoint laws at appendix.tex:1354-1357 stay in Measure.map form and remain separate from the regular conditional-law theorem.
2. The conditional drift at appendix.tex:1368-1377 must use the same named hat rho_s marginal as the weak FP statement at appendix.tex:1379-1387.
3. Cycle 75 identified Mathlib's swapped condDistrib orientation (hat X_s,X_k^eta); cycle 76 packages that orientation with the existing endpoint Measure.map handoffs under explicit supplied-kernel hypotheses.
4. Regular conditional law construction, vector-valued conditional expectation, density/AC, weak FP, KL differentiation, LSI/KL/FI, DV, Gronwall, and theorem closure remain obligations.

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. Reuse the endpoint Measure.map handoff for hat rho_{s_k}=rho_k^eta and hat rho_{s_{k+1}}=rho_{k+1}^eta.
3. 3. Reuse the swapped conditional-law orientation for X_k^eta | hat X_s, but bridge it back to the paper's (X_k^eta,hat X_s) joint-law orientation before weak FP.
4. 4. Do not reopen Gronwall/DV/LSI, display algebra, source-index rebaseline, or theorem-route audits.

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1: preserve appendix.tex statements and source labels exactly, with sald_version_2.tex excluded.
2. Do not add endpoint, standard-Borel, finite-measure, measurability, integrability, or density hypotheses to theorem statements; keep them as backend obligations.
3. Use lean-stat-learning-theory only as a local Mathlib style reference; no Lake dependency or SLT formalization claim.

nonGoals : List String (explicit)

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

Ordered data items

1. No construction of condDistrib, condExpKernel, regular conditional expectations, weak Fokker-Planck, or KL differentiation.
2. No theorem status promotion for thm:forward-KL-discrete, thm:general-moving-target-SALD-discrete, or the EM backend.
3. No broad reusable API work and no project-article export.

lowerPacket : List String (explicit)

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

Ordered data items

1. Target SALD.generalMovingTargetDiscreteEndpointMeasureMapToSwappedConditionalCompatibility.
2. Supply only explicit hypotheses: endpoint a.e. interpolation identities, named rho_k/rho_{k+1}/hat rho_s Measure.map representations, swapped kernel compatibility, and a bridge from swapped joint-law compatibility to the paper's original orientation.
3. Return endpoint equalities, the named hat rho_s marginal in both the swapped first-marginal view and the paper's original second-marginal view, the Measure.map swap equality, and original-orientation kernel compatibility for the weak FP interface.
4. If blocked on the analytic kernel theorem, record that missing theorem narrowly; do not switch to weak FP proof search.

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. New proof-producing work is only local Measure.map endpoint/orientation packaging under supplied kernel hypotheses.
3. Conditional-law construction, weak FP, KL derivative, density/AC, LSI, DV, Gronwall, and theorem contracts remain below formalized.
4. No SLT import, Lake dependency change, sald_version_2.tex use, or source-label drift.
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.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation
2. SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation
3. SALD.generalMovingTargetDiscreteHatRhoFirstMarginalOfSwappedJointMap
4. SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfSwappedComponents
5. SALD.generalMovingTargetDiscreteEndpointMeasureMapToSwappedConditionalCompatibility
6. SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility
7. AutoSamplingTheory.lawMapProdSwap
8. SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract
9. SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface
10. sald.general_moving_target_discrete.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 cycle76GeneralMovingTargetDiscreteEndpointConditionalUpperPacket :
    MainSkeletonAnalyticInterfaceLedger where
  sourceBlock := saldGeneralMovingTargetDiscreteKlWeakFpHandoffSource
  objective := "Global phase judgment: cycle 75 passed reviewer/build and needs no recovery; Phase 1 theorem-skeleton translation is stable enough for cited-theory backfill; the single lower packet that now reduces the largest proof risk is endpoint-law-to-conditional-law compatibility for sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, especially the bridge from endpoint Measure.map laws to the swapped condDistrib orientation needed by the weak FP interface."
  sourceLabels := [
    "proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative",
    "proof:thm:general-moving-target-SALD-discrete:conditional-drift",
    "proof:thm:general-moving-target-SALD-discrete:weak-conditional-fp",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "thm:forward-KL-discrete",
    "thm:general-moving-target-SALD-discrete"
  ]
  analyticInterfaces := [
    "The endpoint laws at appendix.tex:1354-1357 stay in Measure.map form and remain separate from the regular conditional-law theorem.",
    "The conditional drift at appendix.tex:1368-1377 must use the same named hat rho_s marginal as the weak FP statement at appendix.tex:1379-1387.",
    "Cycle 75 identified Mathlib's swapped condDistrib orientation (hat X_s,X_k^eta); cycle 76 packages that orientation with the existing endpoint Measure.map handoffs under explicit supplied-kernel hypotheses.",
    "Regular conditional law construction, vector-valued conditional expectation, density/AC, weak FP, KL differentiation, LSI/KL/FI, DV, Gronwall, and theorem closure remain obligations."
  ]
  theoremRoute := [
    "1. Stay inside appendix.tex:1358-1387 and the existing sald.general_moving_target_discrete.em_interpolation_fp backend.",
    "2. Reuse the endpoint Measure.map handoff for hat rho_{s_k}=rho_k^eta and hat rho_{s_{k+1}}=rho_{k+1}^eta.",
    "3. Reuse the swapped conditional-law orientation for X_k^eta | hat X_s, but bridge it back to the paper's (X_k^eta,hat X_s) joint-law orientation before weak FP.",
    "4. Do not reopen Gronwall/DV/LSI, display algebra, source-index rebaseline, or theorem-route audits."
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1: preserve appendix.tex statements and source labels exactly, with sald_version_2.tex excluded.",
    "Do not add endpoint, standard-Borel, finite-measure, measurability, integrability, or density hypotheses to theorem statements; keep them as backend obligations.",
    "Use lean-stat-learning-theory only as a local Mathlib style reference; no Lake dependency or SLT formalization claim."
  ]
  nonGoals := [
    "No construction of condDistrib, condExpKernel, regular conditional expectations, weak Fokker-Planck, or KL differentiation.",
    "No theorem status promotion for thm:forward-KL-discrete, thm:general-moving-target-SALD-discrete, or the EM backend.",
    "No broad reusable API work and no project-article export."
  ]
  lowerPacket := [
    "Target SALD.generalMovingTargetDiscreteEndpointMeasureMapToSwappedConditionalCompatibility.",
    "Supply only explicit hypotheses: endpoint a.e. interpolation identities, named rho_k/rho_{k+1}/hat rho_s Measure.map representations, swapped kernel compatibility, and a bridge from swapped joint-law compatibility to the paper's original orientation.",
      "Return endpoint equalities, the named hat rho_s marginal in both the swapped first-marginal view and the paper's original second-marginal view, the Measure.map swap equality, and original-orientation kernel compatibility for the weak FP interface.",
    "If blocked on the analytic kernel theorem, record that missing theorem narrowly; do not switch to weak FP proof search."
  ]
  reviewerChecklist := [
    "The active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387.",
    "New proof-producing work is only local Measure.map endpoint/orientation packaging under supplied kernel hypotheses.",
    "Conditional-law construction, weak FP, KL derivative, density/AC, LSI, DV, Gronwall, and theorem contracts remain below formalized.",
    "No SLT import, Lake dependency change, sald_version_2.tex use, or source-label drift.",
    "python3 tools/astis.py source-index ASTIS-SALD-001 and python3 tools/astis.py check pass."
  ]
  dependencies := [
    "SALD.cycle75GeneralMovingTargetDiscreteConditionalLawBackfillLowerObligation",
    "SALD.generalMovingTargetDiscreteEmEndpointMeasureMapPairOfNamedInterpolation",
      "SALD.generalMovingTargetDiscreteHatRhoFirstMarginalOfSwappedJointMap",
      "SALD.generalMovingTargetDiscreteConditionalKernelRegularityOfSwappedComponents",
      "SALD.generalMovingTargetDiscreteEndpointMeasureMapToSwappedConditionalCompatibility",
      "SALD.generalMovingTargetDiscreteEndpointMeasureMapToConditionalCompatibility",
      "AutoSamplingTheory.lawMapProdSwap",
      "SALD.generalMovingTargetDiscreteEndpointConditionalCompatibilityContract",
      "SALD.cycle74GeneralMovingTargetDiscreteConditionalKernelMeasureInterface",
      "sald.general_moving_target_discrete.em_interpolation_fp"
  ]
  status := ProofStatus.obligation

/-- Cycle-76 upper obligation for the endpoint-to-conditional backfill. -/