Phase-Locked Extreme Compression in Adjacent Zeta-Zero Spacing: A Seam-Stitched Empirical Study Through the Full Available LMFDB Horizon

We study rare extreme compressions in adjacent spacing between consecutive nontrivial zeros of the Riemann zeta function on the critical line using a seam-stitched observational board built from the full available LMFDB horizon. Raw zero data are converted into fixed-resolution local spacing summaries with explicit carry-state preservation across shard boundaries, so that adjacent-zero gaps crossing file seams are retained rather than discarded. On this board we define a fitted local spacing spine and a row-level compression score, then isolate connected packets of the most extreme compressions under frozen morphology rules.

The principal empirical finding is that these packets are not phase-neutral. Across broad-board resolution ablations at 130k, 90k, 70k, and 52k zeros per row, the dominant organizing coordinate remains the first logarithmic harmonic
\[
h_1(T)=\left\{\frac{\log(T/2\pi)}{\pi}\right\},
\]
with stable packet concentration statistics and stable continuation-family selection in the trimmed late-stage continuation audit. In every broad-board run tested, the best continuation family for both the local drift coefficient $b_1$ and the local curvature coefficient $b_2$ was quadratic.

A terminal-band comparator on the final 28.5B to 31.5B segment strengthens this picture. On that band alone, the first harmonic remains dominant at 52k, 8k, and 1k resolution, with resultant values approximately $0.999202$, $0.999315$, and $0.999165$, and Arc80 widths approximately $0.017055$, $0.015305$, and $0.015836$, respectively. Thus the terminal tightening is a property of the terminal band itself rather than a 1k-only micro-resolution artifact. Moreover, the 8k board slightly outperforms both 52k and 1k in concentration width, suggesting a mesoscopic scale of maximal coherence within the observed terminal band rather than a trivial monotone dependence on ruler size. In the 1k terminal micro-board, the seam bridge at 28{,}505M remained small, with a fitted-residual jump of order $10^{-7}$, while trimmed late-stage continuation again selected quadratic models for both $b_1$ and $b_2$. Short forward extrapolations just beyond the observed edge remained smooth, with $b_1$ positive near $1.04\times 10^{-5}$ and $b_2$ negative near $-1.70\times 10^{-10}$.

The empirical claim of this revision is intentionally narrower and stronger than in earlier drafts: rare extreme compressions organize reproducibly in the first logarithmic harmonic, this organization is stable under substantial row-size ablation, and the terminal band exhibits unusually tight local $h_1$ locking. We do not claim a closed asymptotic law beyond the observed horizon