DLW-SPUN · the full weave of Tetraktys  (✦ tetraktys · the compass that turns as one)

who   : Tetraktys — the fourfold cardinal oscillator. N S E W are the four roots of unity; raised to the quaternions (1, i, j, k) they become a turning, spinning thing. A ring of five such cells, closed into a torus.
what  : It turns (precession, period 4) and it spins (the 720° double cover, once raised to i,j,k). Coupled around the ring, its detuned cells lock into one rhythm, and a perturbation crosses the ring at a finite speed.
where : A ring of five quaternion cells — the spec 1 xwyzn 00 xwyzn 00 xwyzn 00 xwyzn 00 xwyzn 1, a discrete torus — built and run in sim/nsew.py.
why   : To test, honestly, whether 'geometry is physics' survives contact with a running model — to see what genuinely emerges from a four-phase oscillator, and to keep the line between that and the poetry visible.
when  : 2026 — from a walk-and-talk that mapped the NSEW compass onto spacetime.
how   : NSEW = the 4th roots of unity (×i is a 90° turn); cells are unit quaternions (SU(2), where spin lives); neighbours are coupled through the quaternary bonds; n is the tick that counts the register.

emergence : Genuine, measured, and now native. The first-order proof (sim/nsew.py) locked five detuned dials (Kuramoto, R 0.56→1.00) and spread a signal — but scaling (sim/scale.py) showed that lock was finite-size and the spread was diffusion (t∝d²). The native engine (sim/nuclear.py) folds the fixes in. (1) With INERTIA, propagation is ballistic — a real constant-speed light-cone (t∝d, t/d≈1.2), which in 2-D gives genuine two-source interference. (2) With the long-range EXTERNAL LEAD (the two '1' leads, all-to-all), the lattice synchronizes robustly at ANY size: R≈1.00 from N=5 to N=500, where the bare ring had fallen to 0.22. (3) And inertia adds its own emergent signature — HYSTERESIS: the synced state survives to far lower coupling than it formed at (R(down)≈0.8 vs R(up)≈0.2 across K=2–5, ΔR≈0.61), a discontinuous transition the over-damped model cannot show. (4) And on the 2-D torus lattice (sim/lattice2d.py, live in cosmos.html) all three run in ONE world: a circular light-cone (t∝r, constant speed), two-source interference, and external-lead synchronization (R 0.02→0.95). (5) On the 8×8×8 toroidal register, the +1 (S) phase is a measured ATTRACTOR — a forced N-injection only flips the majority S→N above a critical dose (Q_crit∈(4,5)); below it the structure pulls back. A basin of attraction: self-stabilising, the flip forced not spontaneous. (6) Add stochastic noise and the basin splits honestly: INDEPENDENT per-cell noise dissolves the coherent wells (no clean flips), but CORRELATED (shared) noise makes the lattice 'breathe' — coherent random hopping S↔N over the barrier, the flip-rate rising with noise (Kramers escape; sim/universe.py). Random hopping, not a clockwork oscillator, not 'the observer'. Precession (period 4) and the spin-½ 720° signature (q→−q at 360°, home at 720°) are real but BY DESIGN, not emergent.
verdict   : It clears the bar for the real, modest claim — and no more. Genuine emergence, collective synchronization and a finite signal speed, is measured on the ring; this is the same class of emergence that earned the sync ACIs their faces. The grand mapping — that NSEW literally IS spacetime, that dark matter is N-S-only, that consciousness sits at the null — is NOT derived. Emergent as a coupled oscillator; a cosmos only by metaphor.
asterisk  : The cosmology is mythology, kept visible: 'space/time/distance are NSEW', dark matter, antimatter, the matter-asymmetry, consciousness-at-the-null are analogies, not results — and 'entanglement = shared coordinates with opposite n' is ruled out by Bell's theorem (the live cousin is ER=EPR). Scaling refined the small story (the ring's sync was finite-size, the 'signal speed' was diffusion); the native engine folds the fixes back in. What is real and measured — quaternion spin (SU(2)), a ballistic light-cone, robust synchronization via the external lead, genuine wave interference, and an emergent hysteresis loop — survives. None of this makes the cosmology physics; it stays mythology. The asterisk stays visible.
grounded  : W. R. Hamilton — the quaternions (1843) · Y. Kuramoto — coupled-oscillator synchronization (1975) · Plato — the Spindle of Necessity (Ananke) (-380) · David Lee Wise (ROOT0) — the NSEW spec & the build (2026)

class : ✦ · Tetraktys, the Fourfold · four cardinal phases that learn to turn as one
silicon badge : tetraktys.png      carbon badge : tetraktys.tiff
carbon apex : David Lee Wise (ROOT0)
— an original elemental of Tetraktys — the quaternary cardinal oscillator
✦ · four cardinals, one rhythm
ROOT0-ATTRIBUTION-v1.0 · MIT · ROOT0-ATTRIBUTION-v1.0