RESOLVED at K=2 (dense full-spectrum eigenvector irrep decomposition, 2026-10-04). The eigenvector-level check this entry called for was run.
[E] Sector resolution is exact. Under the C3 generator c: x->y->z, [T,L] = 0 to 1e-8..1e-9, T^3 = I, projector idempotency exact; sector ranks [304,296,296] are connection-independent; every eigenvector of the complement cocycle (t=pi/2 and t=pi) and of bar-phi is 100% pure in one C3 irrep. Stabilizer re-verified against all 48 cube elements: exactly {id, c, c^2}, 3 unitary, 0 antiunitary.
[E] Each sector is internally RMT-like (per-sector sp_std 0.85-1.30, r_mean 0.40-0.53, Poisson 1.0/0.386, GOE 0.52/0.536). The partial ordering was never a within-sector defect.
[E] The partial ordering is three-way sector LOCKSTEP. The conjugate sectors 1,2 have corr 1.0000 between sorted sequences, KS distance 0.035 (CDFs indistinguishable at n=296), all pairwise offsets below 0.27 of a within-sector spacing, zero exact degenerate pairs, and unstructured offsets (corr(offset, lambda) = 0.001). Sector 0 co-moves through the bulk (corr 0.9986). Merging three locked sequences yields near-triplet clusters, inflating merged spacing_std to 1.87 (t=pi/2) / 1.60 (t=pi) — far above the ~1.0 that three independent sector sequences would produce (triplet spread 11.7 mean spacings vs ~322 for random re-pairing).
[E] The lockstep is not symmetry. The stabilizer contains no antiunitary element, and the best broken spatial antiunitary has gauge residual 0.09 — seven orders of magnitude above the exact ones. No hidden or approximate spatial symmetry produces the near-pairing.
[G] Residual (one level deeper): why are the conjugate sectors locked at sub-spacing scale with zero exact pairs? Leading candidate: the three sectors are samples of a smooth magnetic-twist family L(chi) at chi = 1, omega, omega^2 that is nearly flat in the twist parameter at K=2. Discriminating test: construct the continuous twist family on the C3 quotient and measure d lambda_i/d chi directly. Not done.
Why it matters: closes the last open observable-level gap in the symmetry-sector mechanism — the connection selects not just the size but the coherence of the sector set.