AutoSamplingTheory.SALD.cycle95DiscreteForwardKlClosurePressureUpperPacket

Data definition / provenance and workflow record

Meaning and type

The result has data type AutoSamplingTheory.SALD.DiscreteForwardKlUpperPacket. A value of this type stores descriptions; it is not a proof of the statements in those descriptions.

def cycle95DiscreteForwardKlClosurePressureUpperPacket :
    DiscreteForwardKlUpperPacket

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.

objective : String (explicit)

Descriptive text even when field names say formula, theorem, inequality, derivative, source gap, or proof.

Global phase judgment: cycle 94 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 remains the active EM backend sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to the conditional-expectation generator pairing and barB divergence/no-boundary theorem at appendix.tex:1368-1387. The thm:forward-KL-discrete pressure test routes through the current EM wrappers, KL/log-ratio mass handoffs, LSI, DV, Gronwall, and accumulated-error interfaces; the first non-wrapper blocker is ASTIS.SALD.cycle94.remaining_barB_divergence_boundary, reused by sald.discrete_forward_kl.em_interpolation_fp before theorem closure.

sourceLabels : List String (explicit)

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

Ordered data items

1. thm:forward-KL-discrete
2. proof:thm:forward-KL-discrete
3. sald.discrete_forward_kl.em_interpolation_fp
4. sald.general_moving_target_discrete.em_interpolation_fp
5. sald.general_moving_target_discrete.kl_derivative
6. SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff
7. SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff
8. SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction
9. ASTIS.SALD.cycle94.remaining_barB_divergence_boundary
10. SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation
11. eq:general_KL_derivative_0_discrete
12. proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative
13. lem:dv_variation
14. lem:gronwall
15. eq:LSI-KL-FI

modeDiscipline : List String (explicit)

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

Ordered data items

1. faithfulPaper Phase 1 only: keep main_body.tex:299-323, appendix.tex:260-592, appendix.tex:1358-1387, and sald_version_2.tex exclusion fixed.
2. Active-backend check: reviewer did not move the packet away from sald.general_moving_target_discrete.em_interpolation_fp; cycle 95 pressure-tests thm:forward-KL-discrete only to locate the next actual blocker.
3. Do not add assumptions to thm:forward-KL-discrete or replace the paper route through EM weak FP, KL derivative, LSI, DV, Gronwall, and accumulated-error display matching.
4. Use Mathlib conditional-kernel, conditional-expectation, Measure.map, Bochner integral, and divergence-theorem APIs as local candidates; lean-stat-learning-theory remains a style reference only and is not imported.

nonGoals : List String (explicit)

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

Ordered data items

1. Do not mark thm:forward-KL-discrete, sald.discrete_forward_kl.em_interpolation_fp, sald.general_moving_target_discrete.em_interpolation_fp, weak FP, KL derivative, LSI, DV, or Gronwall formalized.
2. Do not add another wrapper around hdriftSource, hsourceSigns, hklRaw, hlog, hmass, hfirst, htarget, or the accumulated-error display.
3. Do not work on display algebra, source-index rebaseline, broad reusable APIs, LSI/DV/Gronwall fallback, or unrelated theorem-route audits while the barB divergence boundary remains open.
4. Do not weaken the source signs: keep -div(hat rho_s * bar b_{k,s}) and +(sigma_eta^2/2) Delta hat rho_s exactly as in appendix.tex:1379-1387.

lowerPacket : List String (explicit)

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

Ordered data items

1. Classification: narrows-source-cited-boundary; discharges-supplied-hypothesis only if lower proves one of the two remaining barB facts and removes the corresponding supplied input from the cycle-94 handoff.
2. Middle should synchronize the pressure-test result: current compiled wrappers carry thm:forward-KL-discrete up to the shared EM weak-FP source-sign backend, and the next exact blocker is ASTIS.SALD.cycle94.remaining_barB_divergence_boundary.
3. Lower should target exactly the conditional-expectation generator pairing and divergence/no-boundary theorem behind SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction: prove driftAction phi equals the weak test-gradient pairing against barB from condDistrib, or prove that pairing equals -(driftDiv phi) for hatRhoS * barB.
4. If blocked, lower must name one smaller theorem with source, imports, and hypotheses, such as the condDistrib/condexp generator identity for barB, the weak divergence integration-by-parts theorem, or the boundary/no-flux condition needed by that theorem.

reviewerChecklist : List String (explicit)

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

Ordered data items

1. Check that the upper packet states all three global decisions: no cycle-94 recovery, Phase 1 stable enough for cited-theory backfill, and the barB divergence boundary is the single lower packet.
2. Verify that the active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, not display algebra or broad theorem-route churn.
3. Confirm the pressure-test blocker is named exactly as ASTIS.SALD.cycle94.remaining_barB_divergence_boundary / SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction with source appendix.tex:1368-1387.
4. Reject a new supplied-hypothesis wrapper unless it removes a cycle-94 barB weak-action hypothesis or exposes a strictly smaller source-cited theorem boundary.
5. No source constants, signs, theorem statements, statuses, SLT imports, Lake dependencies, or source labels may change; source-index and ASTIS check must pass.

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 cycle95DiscreteForwardKlClosurePressureUpperPacket :
    DiscreteForwardKlUpperPacket where
  objective := "Global phase judgment: cycle 94 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 remains the active EM backend sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, narrowed to the conditional-expectation generator pairing and barB divergence/no-boundary theorem at appendix.tex:1368-1387. The thm:forward-KL-discrete pressure test routes through the current EM wrappers, KL/log-ratio mass handoffs, LSI, DV, Gronwall, and accumulated-error interfaces; the first non-wrapper blocker is ASTIS.SALD.cycle94.remaining_barB_divergence_boundary, reused by sald.discrete_forward_kl.em_interpolation_fp before theorem closure."
  sourceLabels := [
    "thm:forward-KL-discrete",
    "proof:thm:forward-KL-discrete",
    "sald.discrete_forward_kl.em_interpolation_fp",
    "sald.general_moving_target_discrete.em_interpolation_fp",
    "sald.general_moving_target_discrete.kl_derivative",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpSourceSignsOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpLawDerivativeOfSampleSplitGeneratorBarBActionHandoff",
    "SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction",
    "ASTIS.SALD.cycle94.remaining_barB_divergence_boundary",
    "SALD.cycle94GeneralMovingTargetDiscreteWeakFpDriftActionLowerObligation",
    "eq:general_KL_derivative_0_discrete",
    "proof:thm:general-moving-target-SALD-discrete:weak-fp-to-kl-derivative",
    "lem:dv_variation",
    "lem:gronwall",
    "eq:LSI-KL-FI"
  ]
  modeDiscipline := [
    "faithfulPaper Phase 1 only: keep main_body.tex:299-323, appendix.tex:260-592, appendix.tex:1358-1387, and sald_version_2.tex exclusion fixed.",
    "Active-backend check: reviewer did not move the packet away from sald.general_moving_target_discrete.em_interpolation_fp; cycle 95 pressure-tests thm:forward-KL-discrete only to locate the next actual blocker.",
    "Do not add assumptions to thm:forward-KL-discrete or replace the paper route through EM weak FP, KL derivative, LSI, DV, Gronwall, and accumulated-error display matching.",
    "Use Mathlib conditional-kernel, conditional-expectation, Measure.map, Bochner integral, and divergence-theorem APIs as local candidates; lean-stat-learning-theory remains a style reference only and is not imported."
  ]
  nonGoals := [
    "Do not mark thm:forward-KL-discrete, sald.discrete_forward_kl.em_interpolation_fp, sald.general_moving_target_discrete.em_interpolation_fp, weak FP, KL derivative, LSI, DV, or Gronwall formalized.",
    "Do not add another wrapper around hdriftSource, hsourceSigns, hklRaw, hlog, hmass, hfirst, htarget, or the accumulated-error display.",
    "Do not work on display algebra, source-index rebaseline, broad reusable APIs, LSI/DV/Gronwall fallback, or unrelated theorem-route audits while the barB divergence boundary remains open.",
    "Do not weaken the source signs: keep -div(hat rho_s * bar b_{k,s}) and +(sigma_eta^2/2) Delta hat rho_s exactly as in appendix.tex:1379-1387."
  ]
  lowerPacket := [
    "Classification: narrows-source-cited-boundary; discharges-supplied-hypothesis only if lower proves one of the two remaining barB facts and removes the corresponding supplied input from the cycle-94 handoff.",
    "Middle should synchronize the pressure-test result: current compiled wrappers carry thm:forward-KL-discrete up to the shared EM weak-FP source-sign backend, and the next exact blocker is ASTIS.SALD.cycle94.remaining_barB_divergence_boundary.",
    "Lower should target exactly the conditional-expectation generator pairing and divergence/no-boundary theorem behind SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction: prove driftAction phi equals the weak test-gradient pairing against barB from condDistrib, or prove that pairing equals -(driftDiv phi) for hatRhoS * barB.",
    "If blocked, lower must name one smaller theorem with source, imports, and hypotheses, such as the condDistrib/condexp generator identity for barB, the weak divergence integration-by-parts theorem, or the boundary/no-flux condition needed by that theorem."
  ]
  reviewerChecklist := [
    "Check that the upper packet states all three global decisions: no cycle-94 recovery, Phase 1 stable enough for cited-theory backfill, and the barB divergence boundary is the single lower packet.",
    "Verify that the active lower packet still targets sald.general_moving_target_discrete.em_interpolation_fp over appendix.tex:1358-1387, not display algebra or broad theorem-route churn.",
    "Confirm the pressure-test blocker is named exactly as ASTIS.SALD.cycle94.remaining_barB_divergence_boundary / SALD.generalMovingTargetDiscreteWeakConditionalFpDriftSourceOfBarBWeakAction with source appendix.tex:1368-1387.",
    "Reject a new supplied-hypothesis wrapper unless it removes a cycle-94 barB weak-action hypothesis or exposes a strictly smaller source-cited theorem boundary.",
    "No source constants, signs, theorem statements, statuses, SLT imports, Lake dependencies, or source labels may change; source-index and ASTIS check must pass."
  ]
  status := ProofStatus.obligation

/-- Cycle-95 obligation recording the discrete theorem pressure-test blocker. -/