LESR FINAL STRESS CHECKPOINT — 09V_TAIL_HANDOFF
Date: 2026-09-23
Target: Tail gate [0.003, pi/120] and root6217 positive-rotation completion

CURRENT VERIFIED STATE:
- Paper09U completed:
  LOCAL [0,0.003] = RESEARCH-CLOSED.
- Paper08 defines AREF-TAIL target:
  m(rho) >= A_ref = 0.8349865 for rho in [0.003, pi/120].
- Paper08 composition theorem is arithmetic only; at that time AREF-TAIL was still OPEN.
- Paper08's original target-specific shape ledger:
  200 total root6217 parents
  5 previous Aref parents pruned
  195 active
  split at rho=0.003:
    LOCAL_ONLY = 10
    TAIL_ONLY = 141
    SPLIT_AT_RHO_CUT = 44

IMPORTANT CORRECTION FOUND:
BCODR-LUC-06 corrects Paper08's parent ledger:
- 8 permanent NOT-F3 parents:
  106, 110, 127, 132, 135, 162, 165, 166
- 5 previous Aref parents:
  28, 36, 68, 144, 155
- 5 new Aref-certified parents from BCODR-LUC-06:
  101, 103, 104, 164, 167
- corrected active parent responsibilities:
  200 -> 192 -> 187 -> 182

KEY IMPLICATION:
Tail is NOT yet globally closed merely by Paper08/Cycle16-17 architecture.
We must explicitly determine which of the 182 active parent responsibilities intersect tail [0.003,pi/120], and certify those tail portions against A_ref using the existing finite lower-bound kernel.

SOURCE FILES RETRIEVED / MATERIALIZED:
- BCODR_LUC_06_Corrected_Parent_Shape_Ledger_v0.1.json
- BCODR_LUC_06_Selected_Tail_Aref_Certificate_v0.1.json

NEXT EXECUTION:
1. Parse corrected 200-parent ledger.
2. Select active parents whose rho interval intersects [0.003, pi/120].
3. Separate:
   - fully tail-only parent responsibility
   - crossing parent tail portion
4. Reuse existing box_lower / split_box / NOT-F3 / Aref certificate kernel.
5. Batch certify against:
   A_ref = 0.8349865.
6. Shard and checkpoint parent batches to avoid timeout.
7. If all tail responsibilities close:
   TAIL [0.003,pi/120] = RESEARCH-CLOSED
   then compose with Paper09U:
   ROOT6217 POSITIVE ROTATION = RESEARCH-CLOSED.
8. Publication audit remains separate.

NO CLAIM YET:
- Tail is NOT yet declared closed.
- Root6217 positive rotation is NOT yet declared closed.
- Global Lebesgue remains OPEN.