test(interval): exercise nested branch scheduling

[kim-em]

Summary

• add a live Mathlib-free two-level branch tree
• use the branch side to fork different child policy states
• pin distinct depth-first and breadth-first frontiers after the nested split
• verify both orders settle to the same retained tree with three target leaves

The second source is deliberately irrelevant to the exponential target: this isolates scheduling/accounting behavior and does not claim a useful subdivision benchmark.

Exact reconciliation

• base: 37bda079c4c9974da49c9e8a8559a66d2e671b45 (post-feat(interval): replay pinned exponential tail #9261 main)
• head: 927427ad931b605bf6c3009b7efe0acc0bc4b82c
• preserves the PNT log-table, nested-log, and exponential-tail experiments and all prior interval content
• proof-only Lake freshness exemption is pinned to exact resolved lakefile.lean blob a869c195af5b211b96e848d4f11754abb64ebcc8

Verification

• lake build HexInterval.NestedBranchConformance HexInterval.Experiment.BranchProof HexIntervalMathlib.ReluConformance HexIntervalMathlib.PntLogTableConformance HexIntervalMathlib.PntNestedLogConformance HexIntervalMathlib.PntExpTailConformance HexInterval.SinTenIntervalConformance HexIntervalMathlib.SinTenConformance HexIntervalMathlib.SinTenIntervalConformance (2253 jobs)
• copyright, file-line, DAG, trust-surface, Phase 4, factor-freshness, PNT-inventory, and diff checks
• no added native_decide, axiom, sorry, admit, unsafe, or implemented_by
• fresh exact-head Opus review and exact-head CI required before merge readiness