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Adjacency Theory markAdjacency Theory

Phase 9 · state space, reachability, promotion gate

State-Space Map

AT-0059 → AT-0072. Two states can pass the same identity test and still have no allowed route between them. This lab maps the valid regions, the islands, the corridors and the barriers — and gates every candidate before it is allowed to mean anything.

x₁ ≡ x₂ ⟺ ‖Q(x₁) − Q(x₂)‖ / ‖Q₀‖ ≤ tol,   Q = (x̄, σ², ‖x‖)
Two states count as the same object when their coarse signature agrees within the tolerance we set — a modeling choice, not a claim about physical identity.

Running the seeded state-space sweep…