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Adjacency Theory markAdjacency Theory

Phase 67 · multi-root / load-balanced address fabric · AT-0641 → AT-0656

One root chokes. Many roots breathe.

Phase 66 left multi-user scalability unresolved and found a root-band deadlock in the single-tree fabric. The structural answer is to stop electing one root. The substrate builds K generic BFS trees before any endpoint exists, every node stores K compact O(log N) addresses, and each trip picks a tree using only the addresses it already holds plus a congestion counter at its own node and first hop — no route oracle anywhere. This page runs the exact event-driven simulation on the real cubic graph, and keeps the closed-form queueing estimate quarantined in its own panel where it can predict but never report.

Plain language

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Exact simulation (downsampled)Heuristic layer quarantinedK fixed, storage K·O(log N)Completion does not reach 1Multi-user scalability OPENNo status promotionPhysical evidence NONE

Headline readings · exact layer

Completion gain, K=1 → K=4

F = 16, N = 256 … 4,096

Busiest-node load

sublinear in offered load

Active footprint

on top of O(log N) route

Multi-user scalability

OPEN

Running the exact multi-root simulation in your browser…

Verdict

Status of the programme after this phase is unchanged: LOCALIZED AUTONOMOUS DOORWAY — TOY CANDIDATE / PHYSICAL EVIDENCE NONE. An architecture that disperses traffic is not an architecture that guarantees delivery, and the gate stays open until it does.

Results · AT-0641 → AT-0656