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Adjacency Theory markAdjacency Theory

Phase 56 · the phase speed limit · AT-0493 → AT-0508

Every part of the shortcut must stay cheap, or none of it counts

Seed 493. Phase 55 left one weakness in the physics and one in the method: the two-phase rule was switched by hand, and the advantage was reported as a single ratio. Both are fixed here. A single frozen excitable law now evolves the order field, decides which couplings are accessible, and restores the ordinary phase through its own refractory tail — no external reset exists in the model. And the advantage is decomposed: nucleation, transit, restoration, preparation, debt and action are fitted separately, each one required to converge and to survive a lower-bound audit before it may be called sublinear.

Plain language

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Headline readings

Time ratio

Cost ratio

Verdict

Physical evidence

NONE

One frozen law · the phase wakes, opens, and sleeps by itself

A single local rule: a resting site becomes active beside an active neighbour, stays active for 6 ticks, is refractory for 6, then rests again. The same rule decides which couplings exist — a latent chord carries an interaction only where both of its endpoints are active right now. Restoration is not a reverse trigger; it is the refractory tail of the same law. Nothing on this diagram is decoration: every colour is the stored state of the site at this tick.

tick 0 / 22

Phase

C₀ — ordinary

Order field

active 1

refractory 0

rest 95

Open latent chords

0

of 48 in the substrate

Onset is the seed

The front itself already travels on the substrate, so the causal structure changed at tick 1 — not when the first chord opened. We do not call the interval before that ordinary-local.

The window law · a frozen constant kills transit

Ntransit · frozen windowtransit · window lawordinaryfrozen still wins

The law, written once

Onset · when exactly does the causal structure change?

tickactive sitesopen latent arcsfront radius on Sphase

Two triggers · fundamental order versus emergent order

Events

Arcs

Closed loops

0

Emergent inversions

Energy ledger · background free energy is never free

Ngross actioncrossings servednet per crossingordinary costQ_cost

Robustness across substrates

Verdict

Blockers raised

Results · AT-0493 → AT-0508