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Publication history: 2026-07-24

Original publication entries retain their wording and recorded status. Follow the current research history for later findings and revisions.

22 / 56 days

24 Jul 2026

1 update
  1. Seam & QGEOI
    v534 — the straddle cone executed

    Summary

    THE FIRST DYNAMICAL SELECTION OF THE ALIGNMENT BIT — reflection positivity keeps exactly ONE member of the interacting mark family alive, \delta=\pi/2 with positive coupling; the literal leading-order cone formalization dies; NO marker moves

    Details

    • New module v534 (SEAM.STRADDLE.CONE.01). The 2026-07-23 review-round contract (recorded “not promoted” in entry (X)) is executed, double-verdicted. V2 = ERFOLG — the selection law (the central datum): with independent couplings \lambda_q on the four mark quartets of M(\delta=m\pi/8) and the equivariant (uniform) direction, reflection positivity holds on every admissible cut over the whole grid g\in\{1/32..8\} for exactly one member \times sign: \delta=\pi/2 (m=4) with positive coupling — all four Grams PD (37,0,0) including the previously untested straddled clock axes 7/15, minimum eigenvalue lifted off the free RP boundary (1.78\cdot10^{-6}\to5.5\cdot10^{-5} near g=1/4: the \pi/2 interaction pushes away from the boundary), Gibbs \beta=2 identical [E]. The asymmetric members die: m=2/6 with s=+ already at g=1/32, with s=- from g=1/8. The v529 straddle law refines: asymmetric straddling kills RP, the symmetric straddling of the self-mirror member protects it.
    • V1 = KILL (the literal cone formalization). The leading-order soft-block cone K_{\mathrm{RP}}=\operatorname{Fix}(G_\delta)\cap\bigcap_c\{\lambda: G_c^{\mathrm{lead}}\succeq0\} is empty for every member and both signs (first-order PT via the exact reduced resolvent, Hermitian to 10^{-15}, central-difference regression 2\cdot10^{-8}) — the linear pencil cannot carry the selection; the protection at \pi/2 is nonperturbative. Recoverable leading-order content: the straddled-cut drift signs are exact (\pi/2: +1.4\cdot10^{-4} for s=+, -3.7\cdot10^{-2} for s=-; asymmetric members reversed) — necessary, not sufficient.
    • The exact geometry behind it [E]. \delta=\pi/2 is the unique symmetric-straddle member: stabilizer = the full clock+mirror group (rotations \{0,4,8,12\}, reflection axes \{3,7,11,15\} = four admissible bond cuts, straddled \{7,15\}), the four quartets partition the 16-circle, and every straddling quartet is reflection-closed across its cut with exact sign +1; m=2/6 straddle asymmetrically; odd m carry no bond axis (the typed v521/v525 placement artifact). \operatorname{Fix}(G_\delta) is 1-dimensional throughout: uniform on m=2..6, NS-wrap-twisted (1,-1,1,1)/(-1,-1,-1,1) on the tight members m=1/7. Typed cross-link: the RP-selected member m=4 is exactly the carrier of the v528 twist-class order parameter O=1/2 — the dynamical selector and the kinematic definition point at the same member.
    • Honest fences [C]. One toy, one interaction class (FK quartets), flat-band parent, \deg\le2 OS bases, finite coupling grid — toy-level evidence for the bit's dynamical origin, not a derivation; nothing about the continuum \mathcal A_{\mathrm{hol}} is claimed; WOIT.OS.TWISTOR.01 stays Open, NO marker moves. Transparency: the run-1 preregistered verdict logic conflated formalization and substance (UNENTSCHIEDEN, mismatch typed); run 2 split V1/V2 with no tolerance change and no number changed — note kept verbatim in the probe. Discovery provenance: experiments/tfpt-discovery/seam_straddle_cone_probe.py (15/15, 2026-07-24).
    • Wolfram mirror. Four exact mirrors (stabilizer census, \pi/2 partition + straddle incidence, reflection-closure signs, equivariant Fix rays incl. the wrap-twisted m=1/7 rays) in wolfram/tfpt_readouts_extension.wl, verified engine run 2026-07-24, 584\to588 (the 256-dim Fock spectra, PT corrections and finite-g scans stay Python-only, flagged); suite 527\to528 modules.