one clock: θ drives every view · 1 lap = 8φ = 12.944 = 8φ tP (bridge: 8φ lP at c) · walker 1 step / 36°
L5 walker 0/100cell (0,0)I 0
running
⚠ UNBOUND INTERFACE · LaneBijection
legend
Q.D LAYER · 1 dot per pixel · 2³ = 8 states MODELANALOGY
hover the city to inspect a dot
state = 4·born + 2·shell + sign · sign = ψ sign (− even / + odd) · born = |A(θ)|² ≥ ½ · shell = ring parity
Sapphons · 10 black holes · fight ↔ homeostasis
r_s T_H Sfightcontroller~mP–
Ten black holes in the city (masses in Planck masses mP, lengths in lP), one shared pool of photon energy. They fight: each absorbs A·u/4 from the pool and radiates Hawking power, pulls on the others, and merges on horizon contact. Alone that runs away (negative heat capacity: the biggest eats everything, the small ones evaporate). The homeostasis controller holds ΣM and N at their setpoints. The θ clock drives it: each Planck tick = Λ tP of sim time (steps of 10 tP).
seed
setpoint M*setpoint N*gain Kp (mass)gain Ki (mass)share exponent kΛ (tP per tick)
CONTROLLER error e = M* − ΣM; reservoir → pool at rate Kp·e + Ki·∫e; each hole absorbs η·A·u/4 with η = (m*/m)^k, m* = M*/N* (k > 4 beats the negative heat capacity; try k = 3 to watch it fail); a new hole of m* is seeded from the pool when N < N* and there is room. Sliders apply from now on; rewinding the θ clock past a change brings back the settings of that moment. 2nd LAW S_total = photon gas + Σ A/4 never falls on its own; what the controller takes out is booked as S_ctrl.
Scale dial · Planck, −∞ … +∞
bijectioncity< lP–
u = (2/π)·atan(log10(L / lP) / 30): the whole length axis squeezed into (−1, 1), lP = 1.616255e−35 m (from K) at the centre, −∞ at the bottom, +∞ at the top. Click or drag the bar to read any scale; ▶ is the photon path so far (θ clock).
|<e>| | Re | N | +el · 0.3 p stack
T exactdots ≈sub-atomicT–
A closed ring at r = 840 between the 11 shells (≤ 780) and the photon path (895). Order from the city (− side) outward to the photon (+ side): |<e>| electron sheet, Re, N, +el. Total 0.3 px on screen at every zoom; the 1 px ticks only mark where it is. The dot sign flips (XOR) on entering +el.
E25.0uscale10.0u / eV
· if p = lP: 0.3 lP = m WALL
UNITS ħ²/2m = 1, lengths in p, energies in u = ħ²/(2m·p²); layer height (u) = scale × height (eV). T from the exact transfer matrix for piecewise-constant V (ψ, ψ′ matched at every interface); R + T = 1 is checked. Widths 0.03 / 0.12 / 0.06 / 0.09 p: thinnest for the 2D electron sheet, thickest for the Re slab, electrum next, the N layer as a thin gap. CA each generation every barrier cell is open with probability T (seeded hash), closed cells block the neighbour sum; the rule stays second-order, so forward/back is still exact for fixed T; moving a slider re-derives the history from G0.
Generations · reversible CA
BIJECTIVE≈ QCA–
G 0
grid hash — · — ·
RULE c′ = (N + E + S + W − c_prev) mod 4 on a 512 × 512 torus of cells (each pixel shows the cell under it). Second-order (Fredkin) form, so it is exactly invertible: c_prev = (N+E+S+W − c′) mod 4. The dot shown = v4 state ⊕ (c ≪ 1): the CA flips the born/shell bits only; the sign bit stays the spin-½ sign. One generation = one full 720° cycle. Bars = pixels per colour on screen.
Spinor · SU(2)
MATCH spin-½WALL photon = spin-1–
axis n
U(θ) = exp(−iθ σ·n/2) on ψ₀ = ((−1+i)/2, (1−i)/2). MAPPING his 4 signs = signs of (Re ψ↑, Im ψ↑, Re ψ↓, Im ψ↓). Row 2 = A(θ)·ψ₀ with A = ⟨ψ₀|ψ(θ)⟩ = cos(θ/2) (⊥ axis): −++− → 0000 at 180° → +−−+ at 360° → −++− at 720°, his rule exactly (Rauch 1975; Werner 1975). A photon is spin-1 (gold dashed, home at 360°); for light the SU(2) maths lives in the polarization description and geometric phase (Tomita & Chiao 1986).
Orbit · Z₁₀×Z₁₀ walker
MATCH proven36°/step display–
class
MAPPING 1 walker step (x−2, y+3) per 36° of photon phase, so one orbit (10 steps) closes every lap. The kernel has no time binding; this pacing is display only. Proven: every orbit has length n/gcd(n,a,b) = 10/gcd(10,8,3) = 10, and I = (3x+2y) mod 10 never changes.
Constants · one source
lP/tP = c ✓–
Every view reads this one frozen object (K). Model values from A:\CONSTANTS.txt (lP redecided 2026-09-29 to the measured value); measured values from A:\CONSTANTS_CODATA.txt: CODATA 2018 (Tiesinga et al., RMP 93, 025010), same digits as NIST CODATA 2022. BRIDGE 1 lap = 8φ lP travelled at c = 8φ tP.