Silicon's Two Records: The Count's Third Sound Entry Splits Under Its Own Dispersion

AF-29's close charged the condensed line's remaining unrun test: silicon, AF-4's third sound entry, had never faced the full-dispersion treatment that repaired aluminium's neighbourhood and exposed lead's split — AF-19 had assigned Si to the one-record class on the strength of its single-mean landing (0.996), the same kind of evidence AF-19 itself showed to be compensation in lead's case. This paper runs AF-24/AF-29's construction verbatim for silicon: sine branches through the measured zone-boundary frequencies of the neutron record (Dolling's silicon dispersion, anchors declared to 0.1 THz, ±0.5 THz scanned) along [100], [110], [111] with multiplicity weights 6/26, 12/26, 8/26, and the three standard wall extractions. Declared scope, on the face: silicon's primitive cell is diatomic, so the crystal carries six branches; this filling carries the three acoustic branches — the count it returns (3.0000 per atom) is the acoustic census, and the three optical branches (zone-centre frequency 15.6 THz class) enter the heat capacity at temperatures above the extractions graded here. The results: the moment wall ⟨ω²⟩ = 65.8081 THz² gives θ = 502.6 K (ratio 0.779); the calorimetric match curve's low-temperature end gives θ_CV = 484.6 K at 1 K, flat through 5 K (484.5, 483.2), falling to 478.2 K at 10 K and 450.1 K at 20 K (ratios 0.751–0.698); the ±0.5 THz anchor scan moves the walls to 476.7–528.8 K (moment) and 438.9–529.6 K (match at 1 K) — nowhere near 645 K at either end. The slope probe explains why no averaging defence is available: the sine law's implied initial slopes err in opposite directions on silicon's two [100] branches (LA overstated, 10664 against ~8430 m/s; TA understated, 3839 against ~5840 m/s), so the filling's walls cannot be excused as a one-signed slope artifact of the interpolation — and the low-temperature match, which is slope-dominated by construction, is itself the witness: a dispersion whose true low-frequency content matched the 645 K record would return a match curve near 645 K at 1 K whatever its zone-boundary anchors, and this one returns 484.6 K. The verdict composes with the ledger's: AF-4's count is exact for silicon (3.0000, computed here from the dispersion itself); AF-4's wall for silicon was the product of a declared mean speed (its implied v_m ≈ 5.67×10³ m/s, back-computed from AF-4's printed wall frequency) that is no branch's speed and no record's wall — the same compensation species as lead's 1050 m/s, caught this time in the covalent pair AF-4 called its most honest entries ("negligible where one covalent network makes the average honest" — the sentence does not survive this paper, and §3 prints its correction). Diamond, the pair's other member, is now the condensed table's last untested sound entry, and this paper's F1 names it.