Quark Generations as Icosahedral Boundary Excitations: Particle Masses from Twin Prime Resonance

This document supersedes Paper 18 v1.0 (Quark Generations as Icosahedral Boundary Excitations, January 2026). The original paper proposed quark generations as elastic-proton boundary excitations at icosahedral thresholds 19, 30, and 42, with quark and electroweak boson masses derived from twin-prime product arithmetic. Under the methodological discipline subsequently developed in the programme — Pattern 39 (the distinction between DERIVED and OBSERVED claims) and Pattern 75 (null-hypothesis discipline for numerical matches), with pre-registered testing — the original mechanism does not survive: numerical matches were reported without null distributions, the W boson formula contained an undefined factor-of-40 scaling, the charm and strange quark formulas were arithmetically unmotivated, and the proton mass was used as baseline rather than derived. The geometric aim — quark generations as resonance excitations of a single icosahedral structure — has been substantially realised in a cluster of subsequent papers covering the proton, the pion, the hadron spectrum of light baryons, and the electroweak sector; the specific second- and third-generation quark-mass derivations remain open in that cluster and are flagged there for future work. This notice retires v1.0, names what survives, points to the replacement papers, and is honest about what the cluster has not yet delivered.