Paper 108C: Shell-Ladder Activation Specificity and the Limits of Pure Gate Selection Mirror-Pair, Sign/Orientation, and Closure Tests in the TDR-Graph-Corridor Wilson-Growth Program

This paper tests whether shell activation in the Paper 108 graph-corridor Wilson-growth program is specific to the proposed cuboctahedral mirror-pair structure, sign/orientation compatibility, and admissible closure, or whether nearby broken shell pairs and off-ladder fake-count controls can imitate the same behavior. Papers 108 and 108B established a reduced-support corridor mechanism in which admissibility-constrained shell transport can produce structured Wilson-growth-like diagnostics under controlled lattice conditions. Paper 108C addresses the next concern: whether the successful response depends on a meaningful shell-ladder relation or whether broad activation gates reward many nearby support geometries.

The V7 mirror-pair activation sweep tests three allowed activation classes at L = 16: a Z-like 2-to-5 plus mirror relation, a W-like 3-to-4 minus mirror relation, and a composite 2-to-5 plus / 3-to-4 minus relation. These are compared against broken cuboctahedral mirror controls, including 2-to-4, 2-to-3, 3-to-5, and 4-to-5 pairs, and off-ladder fake-count controls, including 240-to-350, 252-to-400, and 300-to-500. The strict output gate requires B_grow at least 0.004, s12 at least 0.002, and s23 at least 0.002, with either positive Creutz channel accepted. The full V7 run evaluates 19,008 reduced-support rows across six seeds, two replicas, activation thresholds, pair budgets, orientation couplings, closure weights, and budget scales.

The result is a partial positive rather than a final shell-specificity proof. Allowed mirror/composite activations form a reproducible high-pair-budget positive pocket. The best repeated allowed region has allowed fraction 0.479167, control fraction 0.380952, and activation advantage 0.098214, exceeding the declared 0.05 advantage threshold across adjacent threshold and closure cells. However, controls remain competitive. At lower pair budget, several control regions outperform the allowed classes, with allowed fraction 0.208333, control fraction 0.380952, and advantage -0.172619. Therefore, V7 supports activation sensitivity but does not establish full activation specificity.

The main conclusion is constructive. Cuboctahedral mirror-pair structure, sign/orientation, and closure appear to matter, but pure activation gates remain too permissive to identify a final physical binding or confinement mechanism. Paper 108C therefore closes the activation-specificity audit by identifying the failure mode: static activation can separate in some regions while still allowing broken and off-ladder controls to remain competitive. This motivates the Paper 108D pivot from activation gates to finite-distance exchange-renewal and deuteron-diproton truth-table selectivity.