Root Semantics Upgraded from Stored Floats to Exact-Rational Directed Reconstruction: All 9,278 of Cell0's Terminal Leaves Complete Bulk Migration, 9,278/9,278 Pass with Zero Selective Resplits

Round 28 (AMRAL-LUC-FC-R28, 2026-09-20) closes the largest structural gap left by Round 27: Round 27's interval prototype only built an enclosure around the already-stored binary64 leaf state, rather than reconstructing everything from the master root under exact split semantics. Round 28 switches the master target to the exact rational T_M = 1673/2000 (replacing the earlier binary64 value 0.8365), while the certification threshold remains the exact rational T = 167/200; it uses the monotonicity of the a-priori equation F(d) = ¼(π − arccos(1/2d)) + ½√(d² − ¼) on the relevant domain to run a directed interval bisection for d⋆, reaching a final interval width of about O(10⁻⁶³), and reconstructs the translation roots t3, t5, t7 of the regular odd Reuleaux shapes B3/B5/B7 the same way, with interval widths all far below 10⁻⁵⁰; the D3 master root is then built directly from these directed endpoints. Cell0's 40-layer base path no longer depends on re-running the scheduler to infer each cut: the certificate now stores the actual split axis and side bit, so a verifier only needs to check C=C0∪C1 and need not trust the official heuristic, CPG, any learned scheduler, or a cost model — and the measured override count along this path is 0. The B7 lift tree (Round 24 topology: 18,555 nodes, 9,278 leaves) also gets an explicit 2-bit split-axis stream for its 9,277 internal nodes. After reconstruction, the deviation between the stored reference center and the intended center is about 10⁻¹⁷ at most (about 2.1×10⁻¹⁶ for the witness tree), and the document states plainly that "close ≠ identical" — from here on, membership is always decided against the intended directed box, never the stored float. The core numerical result: applying margin-adaptive rational inner-polygon bulk migration to all 9,278 of cell0's terminal leaves (across seven candidate-density tiers — 256/512/1024/2048/4096/8192/16384 — distributed 821/3425/3709/1115/163/39/6, with only 6 leaves needing the highest tier of 16,384) yields 9,278/9,278 RATIONAL-INTERVAL-PASS, zero selective resplits, zero membership failures, and a thinnest exact rational margin of 3.1948922738×10⁻⁸ (matching Round 27's targeted replay); cell0's status is upgraded from REFERENCE-COMPLETE to CELL0-ARITHMETIC-MIGRATED-PROTOTYPE. The document is explicit that this still cannot be upgraded to a global publication theorem: the directed-interval backend (mpmath.iv/libmp) is not yet version-pinned or independently audited, the upper certificates for the 77 necessity markers are not all arithmetically migrated yet, and neither the global base atlas nor the final shard merge yet has an independent A1 replay. Round 28 therefore proposes fixing the root-reconstruction fields into a root-certificate ABI (exact target, exact master target, directed d⋆/t3/t5/t7/D3 intervals, the explicit base axis/side path, witness topology and axis stream, and the arithmetic backend id/hash), explicitly excluding the scheduler's name from the proof-critical bundle. The global bound a_Leb≥0.835 remains an unproven, NOT CERTIFIED open problem, and this round does not change that; the next round, Round 29, is previewed to carry out directed support upper migration for the 77 necessity markers. Research direction and methodology are due to Neo.K; this round's AI collaborating researcher and primary executor was Aletheia / ChatGPT, GPT-5.6 Sol.