The Table Repaired, and a Second Glass: Aluminium, Iron, and the Count That Does Not Move
Year: 2026
Type: preprint
Abstract: AF-4's six-material Debye table had three sound entries (lead 0.955, silicon 0.996, diamond 0.995), one artifact repaired by AF-9 (copper 1.362 → 0.996), and two remaining off-ratios: aluminium 1.167 and iron 1.113. This paper applies AF-9's branch-resolved pattern to both — measured longitudinal and transverse sound speeds combined as the low-temperature wall requires, 1/v_m³ = (1/3)(1/v_l³ + 2/v_t³), on AF-4's own densities and molar masses. Iron repairs completely: v_m = 3614.6 m/s returns θ_D = 472.9 K against the measured 470 K, ratio 1.006, its distance collapsing from 0.113 to 0.006. Aluminium repairs most of the way: v_m = 3420.4 m/s returns 399.3 K against 428 K, ratio 0.933 — the distance more than halves (0.167 → 0.067) but does not close, and the remainder is printed unexplained rather than absorbed: branch resolution is not the whole of aluminium's filling, the way it was the whole of copper's and iron's. The paper then extends AF-9's optics count to a second glass: fused silica's visible dispersion is again a Sellmeier sum of exactly 3 oscillators, at different addresses (0.068, 0.116, 9.896 μm against BK7's 0.077, 0.141, 10.176 μm), Abbe number 67.79 against the record's ~67.8. Across two glasses the count is the invariant; the address list is the material.
Author: Aldred, William Alexander
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225398349