One rule, three coordinates, nine settled digits.
One rule governs everything on this page: the address must predict itself. A universe of coupled oscillators computes its own coherence, which determines the coupling, which determines the coherence. The loop must close. Where it closes is the address.
Three coordinates locate us within that fixed point.
Clocks count iterations — when we are. Depth spans the scale hierarchy from the fastest oscillation in nature ($10^{43}$ Hz) to the slowest ($10^{-18}$ Hz) — where we are. Expansion measures how much of the frequency axis has synchronized — how far the computation has progressed. The 18.7% that remains unlocked is the gap, and the largest gap sits at $1/\varphi$.
After 13.8 billion years, 9 digits of the coherence parameter $|r|$ have settled. This page is the printout so far.
Four hands, one face. The rose hand shows 0.95 of one Hubble cycle — when this iteration's computation resets. The green hand marks our observation window at level 21 of 145.8. The blue hand tracks how much of the frequency axis has locked. The dashed gold hand is the gap twin at $1/\varphi$, accumulating phase at $10^{-59}$ radians per oscillation.
A golden spiral from Planck frequency (center) to Hubble frequency (edge). Landmarks appear where oscillations have synchronized at observable scales.
Temperature fluctuations in the CMB are the imprint of the observation window: $\sqrt{5} = 2.236$ levels wide, centered at level 21. This is where our 9 settled digits become measurable.
THE COMPUTATION
8 steps. Three coordinates, one rule. 9 digits of $|r|$ have locked so far.
The age is derived from the number of completed cycles via Friedmann integration, not an input parameter.
Digits available: 9
The recurrence $x_{n+1} = 1/(1+x_n)$ has completed 47 iterations. Each settles one more ratio at the convergence rate $2/\pi \approx 0.6366$ per Hubble cycle. The coherence parameter $|r|$ is determined to 9 significant digits.
The next self-consistency checkpoint is iteration 76 ($L_9$, the next Lucas number), where $\varphi^n + \psi^n$ is again an integer and a new set of predictions becomes simultaneously confirmable from both roots. At the current Hubble rate, that is approximately $8 \times 10^9$ years from now.
The Minimum Self-Predicting Universe
Self-consistency: the fixed point $x = f(x)$ is where the computation terminates. The address must predict itself.
$N = N_{\text{total}} \times g \times w(K_0 F[N])$
Four primitives: Z (integers) · mediant · fixed point · parabola
The rule is not derived from the coordinates. The coordinates are consequences of the rule. Self-consistency uniquely determines where the loop closes.
The recurrence $x_{n+1} = 1/(1+x_n)$ has two roots: $\varphi$ and $-1/\varphi$. Their product is $-1$. Three dimensions where the arms reinforce, one where they cancel — spacetime signature $(3,1)$.
$\sin^2\theta_W = 8/35 = 0.2286$
Two loops share one crossing point. 8 cross-sector transitions = 8 gluons. The crossing fraction gives the Weinberg angle.
Coupled oscillators lock along the path of least resistance. Simple ratios first, complex ratios later. The gaps — 18.7% of the frequency axis — are where coherence has not yet been reached.
$\text{width}(p/q) \propto K^q / q^2$
The gap twin at $1/\varphi$ accumulates phase at $10^{-59}$ radians per oscillation. It will take $5.6 \times 10^{68}$ years to register a single bit.
Two binary choices (locked/unlocked × twist locked/unlocked) produce four states. Three observable, one dark — spacetime signature $(3,1)$.
3 observable + 1 dark = (3,1)
$i^2 = -1 = J^2$ = double half-twist
Three generations = three spatial dimensions = $2^2 - 1$. The dark state is the unobservable fourth phase.
Every row below follows from the three coordinates and the rule. $|F_6| = 13$ locked modes, 12 coupling channels, four phase states giving $(3,1)$ signature. No free parameters.
$\Omega_\Lambda$ = (11 + 2w*) / (16 + 3w*) = 0.6847
$\alpha_s / \alpha_2 = 27/8$
Every row is derived from the three coordinates and the self-consistency rule. No fitted constants. The residuals measure distance from experiment, not from a fit.
13 modes · 12 channels · 4 states · 3 dimensions · 1 dark · 0 parameters