Skip to main content

A registered result in its source context

Original ledger classification: V1=KILL / V2=ERFOLG ([E] exact integer/Fraction census + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves

Recorded statement: THE RP CONE ON THE INTERACTING FK QUARTETS -- THE FIRST DYNAMICAL SELECTION OF THE ALIGNMENT BIT (2026-07-24; one module, 15 checks, ~7 s; double-verdicted; the named v534 candidate of the 2026-07-23 review round executed). V1 = KILL, V2 =…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

SEAM.STRADDLE.CONE.01

Original ledger classification: V1=KILL / V2=ERFOLG ([E] exact integer/Fraction census + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves

Original claim text

THE RP CONE ON THE INTERACTING FK QUARTETS -- THE FIRST DYNAMICAL SELECTION OF THE ALIGNMENT BIT (2026-07-24; one module, 15 checks, ~7 s; double-verdicted; the named v534 candidate of the 2026-07-23 review round executed). V1 = KILL, V2 = ERFOLG. (1) V1 = KILL (the literal contract formalization): independent couplings lambda_q on the four mark quartets of M(delta), leading OS-Gram correction dG via first-order PT (exact reduced resolvent of the gapped flat-band parent; Hermitian to 1e-15, central-difference regression 2e-8) -- the soft-block cone K_RP = Fix(G_delta) cap {lambda: G^lead >= 0 on every admissible cut} is EMPTY for every member and both signs: the linear-pencil formalization cannot carry the selection. Recoverable leading-order content: on the STRADDLED cuts the drift sign pattern is exact -- pi/2 has POSITIVE drift for s=+ (+1.4e-4 on both straddled clock axes) and strongly negative for s=- (-3.7e-2); the asymmetric members have it REVERSED (m=2 s=+: -1.9e-2; s=-: +1.1e-4). (2) V2 = ERFOLG (THE SELECTION LAW, the central datum): among ALL well-posed members x coupling signs of the equivariant FK family exactly ONE combination keeps reflection positivity on every admissible cut over the entire grid g in {1/32..8}: delta = pi/2 WITH POSITIVE COUPLING -- all four Grams PD (37,0,0) including the v529-UNTESTED straddled clock axes 7/15, minimum eigenvalue LIFTED from the free boundary 1.78e-6 up to 5.5e-5 near g=1/4 (the pi/2 interaction pushes the Gram AWAY from the RP boundary); m=2/6 with s=+ violate RP 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. (3) EXACT GEOMETRY: delta = pi/2 is the UNIQUE symmetric-straddle member -- stabilizer = full clock+mirror group (rot {0,4,8,12}, refl {3,7,11,15} = FOUR admissible cuts, straddled {7,15}), quartets PARTITION the 16-circle, every straddling quartet reflection-CLOSED with exact sign +1; m=2/6 asymmetric (two cuts, one straddled); odd m no bond cut (typed v521/v525 artifact); Fix(G_delta) 1-dim throughout -- uniform ray on m=2..6, NS-wrap-TWISTED signed ray on the tight members m=1,7. (4) TYPING + CONTROLS: leading order NECESSARY (negative straddled drift kills at g=1/32) but NOT SUFFICIENT (m=2/6 s=- carry positive drift yet die at 1/8; only pi/2 extends -- the protection is NONPERTURBATIVE); every avoiding cut PD for every member/sign/g; Gibbs beta=2 reproduces the pattern on all four pi/2 cuts both signs; non-equivariant lambda=e_0 breaks well-posedness (dev 0.11 -- Fix does real work); clock-pair spectra identical to 4.4e-15; v529 B3 anchors reproduced. TYPED CROSS-LINK (no claim): the RP-selected member m=4 is exactly the carrier of the v528 twist-class order parameter O=1/2 -- dynamical selector and kinematic definition point at the SAME member. MANDATORY FENCE: ONE toy, ONE interaction class, [C] flat-band parent, deg<=2 OS bases, finite grid -- toy-level evidence FOR the bit's dynamical origin, NOT a derivation; nothing about the continuum A_hol is claimed. Transparency: 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.

Original classification detail

V1=KILL (the literal leading-order cone formalization is empty everywhere); V2=ERFOLG (THE SELECTION LAW: RP holds for exactly ONE member x sign -- delta=pi/2 with positive coupling; asymmetric members die; straddle law refined: symmetric straddling protects); first dynamical selection of the alignment bit at toy level; [C] fence one toy/one class; no marker moves

Dependencies as recorded

SEAM.INT.FKTOY.01; SEAM.BIT.TWISTCLASS.01; WOIT.OS.TWISTOR.01; WOIT.BETA2.OS.01; SEAM.BIT.TWISTBLIND.01; v510; v519; v524; v528; v529

Open the original ledger source, row 597

Location recorded in the ledger

These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.

Sections that explicitly cite this claim

A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.

All 18 linked sections

Navigation through a shared verification script

These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.

All 41 linked sections

Registered verification modules

  • v534_seam_straddle_cone.pyRegistered verification module · frontier
    Read the description recorded in the module registry

    SEAM.STRADDLE.CONE.01: the RP cone on the interacting FK quartets — the FIRST DYNAMICAL SELECTION of the alignment bit (15 checks, ~7 s). V1=KILL: the literal leading-order cone is empty everywhere (linear pencil cannot carry the selection; recoverable content = the straddled-cut drift sign pattern). V2=ERFOLG — THE SELECTION LAW: reflection positivity holds for EXACTLY ONE member × sign of the equivariant FK family — δ=π/2 with positive coupling, PD (37,0,0) on all four cuts incl. the untested straddled clock axes 7/15 for g∈{1/32..8}, min eigenvalue LIFTED off the RP boundary (1.78e-6 → 5.5e-5); asymmetric members die (s=+ at 1/32, s=− from 1/8). Exact geometry: π/2 = the unique symmetric-straddle member (quartet partition, reflection-closed straddles sign +1, four admissible cuts); Fix rays measured. Typed cross-link: the selected member m=4 carries the v528 twist-class order parameter O=1/2. [C] one toy / one interaction class; NO marker moves.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries