The Model

Reading the model

Let it run. The sweep carries k across the cascade band and loops: near the quantum end the field is dark shimmer — actualization is attempted fast and nothing persists; through the critical zone the red form ignites and strobes as one thing against the background; at the classical end everything glows steadily and the strobe washes out into stable matter. Take either slider at any time. Manual mode holds a k while you work the other controls; speed scales the sweep and the dynamics together, on one clock.

Nothing is scripted

Every dot is an antipodal possibility-pair running the same τ-cycle the Arena page shows, as a noisy oscillator among thousands. Exactly four quantities vary with k, each monotone: the actualization rate rises, persistence rises, phase noise falls, and the coupling that integration applies scales with the rate. No regime is programmed anywhere in the code — the dark quantum end, the ignition through the critical zone, the classical washout, and every number the meter reports are consequences the dynamics produce. The mappings are scaled for legibility and the slider's traverse is normalized; on the framework's own scale the critical zone sits roughly at k = 54 to 76 of the cascade, and the derivations are in the technical reference.

The criticality meter

The meter reports one number, C: how much the form coheres apart from the surrounding field, times how sharply its actualizations still strobe. The two factors fail in opposite directions — noise destroys coherence on the quantum side, saturation destroys the strobe on the classical side — so C is peaked, and the dashed line marks the working criterion for criticality. The curve of C against k is drawn live from measurement, only where the slider has actually been. Set integration to zero and C lies flat at zero across the entire scale: no position rescues it.

Integration, binding, and the form

Integration is a continuous gain on the coupling between neighboring sites, and it has its own threshold: sliding it up changes nothing, then the form snaps into lock — a second phase transition, on an axis orthogonal to k. Binding is a diagnosis rather than a control: it draws an edge between two neighbors only when the dynamics have phase-locked them and they actualize together, repeatedly. With integration off it stays dark. The form is the content being actualized — an apple-shaped region whose sites are sampled denser, matter being denser than vacuum, with a narrowed frequency spread and colors fixed at the start as content, red body and green leaf. A deposit renders as its content color times a brightness the dynamics alone determine, so the colored apple appears exactly insofar as its sites actualize. Turn the form off and a faint density ghost remains, but nothing again actualizes as one thing.

One band of the cascade

A bound, integrated whole — many separate events acting as one — has a place on the cascade: one band of it, set by the same geometry that fixes the particles and the forces. Biology exploits conditions like these; what the model puts on screen is the physics underneath them. For a plain-language introduction, see the Explainer; the full development is in the technical reference.

The same τ-cycle, read at the scale of the universe. One geometric ladder carries k from the Planck scale to the present epoch, and the gauges beside it report what that geometry produces at each rung: cumulative actualizations, effective gravity, ambient temperature, energy and information per event, and the resolvability that sets a single event against the thermal noise around it. Sweep it and watch resolvability descend toward the band where bound, integrated wholes can hold.

Reading the model

Let it run, or take the k slider and move through the cascade yourself. Early on the disc churns fast and stays sparse — hot, quantum, high-rate actualization with little persistence. Through the middle the rate eases and tiles begin to hold their state. Watch the gauges cross the marked thresholds; watch the disc's texture as the cascade reaches the critical zone. Integration runs on by default; the integrate control switches it off. The coupling only acts inside the critical zone, so outside that band the disc runs the same whether integration is on or off — the difference is something to watch for as the cascade crosses the zone.

The thresholds and capacities are framework values; the timing and rate mappings are tuned for legibility. The behavior it runs — actualization, the cascade, coupling forming and dispersing — is the framework's. The derivations and exact values are in the technical reference; for a plain-language introduction, see the Explainer.

What the model shows

The disc is RP³, the grain of actuality. Each tile is a region of it. A tile glowing gold holds a settled fact; the violet haze behind the disc is the CP³ possibility those facts are drawn from; and every cyan flash is a τ-event — one projection from possibility to actuality, one point made definite.

The ladder beside it is the cascade index k — a position on the framework's energy hierarchy, each rung a fixed geometric step anchored by the pion mass. The cascade is a single scale, and to descend it is to trace, at once, the thermal history of the universe, the Standard Model's chain of symmetry breaking, and the passage from quantum indefiniteness to classical fact. One geometry sets that scale, so these descend together. The ladder runs from the Planck scale at k=1, through the unification and electroweak thresholds and quark confinement, to the present epoch near k≈80, and on into the deep future. The marked rungs are where the structure of matter changes.

The gauges read what the geometry produces at the current rung. M(t) is the running tally of τ-events the universe has actualized — about 10¹²¹ by the present. G_eff is the effective gravitational coupling inside collapsed structure, stronger at high redshift and easing toward its present value as the cascade runs, (1+z)³ᐟ²; the constant that sets cosmological expansion is separate and fixed. Ambient temperature falls from the Planck scale toward today's 2.7 K. E(k) is the energy of a single τ-event at that rung. Resolvability, R, sets that energy against the ambient thermal noise, k_BT, and the information a single event carries grows with it. Entropy per event, by contrast, never moves — about 5.5 k_B at every rung — fixed by the geometry of the projection rather than by the scale.

Actualization

Watch one tile. It carries a phase that advances steadily; when the phase completes a turn the tile fires — a τ-event, the cyan flash, possibility made actual. Then it fades. Fading is decoherence: the fact loses definiteness and the tile dims back toward possibility, until its phase comes round again and it re-actualizes. The whole disc is a field of these cycles running at once, at a rate the cascade sets — fast and hot near the Planck scale, slow and cool toward the present. Left to themselves the cycles run independently, and the disc shimmers without pattern.

The critical zone, and integration

Resolvability splits the cascade into three regimes. Where R is large, τ-events stand sharp against the thermal background; where R is small, they are washed out by it. The critical zone is the band between — roughly k=54 to 76 — where R passes through order unity and a single event carries about as much as the noise around it. The resolvability sub-band marked inside it, k≈71 to 76, is where that balance is tightest.

That balance is what integration needs. With integration engaged — the model runs with it on — the tiles stop firing independently. Each τ-event begins to draw on the ones beside it, and as the cascade enters the critical zone the disc's shimmer organizes: the flashes find each other and fall onto a single, manifold-wide beat. The synchrony holds only while R stays near unity, per-event signal and thermal noise in balance. Past the resolvability window R sinks below one — thermal noise overruns the signal, the per-event information channel closes, and the coherent beat washes back out into shimmer.

A bound, integrated whole — many separate events acting as one — has a place on the cascade: one band of it, set by the same geometry that fixes the particles and the forces. Biology exploits conditions like these; what the model puts on screen is the physics underneath them.