Long-Horizon Architecture.

A framework for structural admissibility, drift navigation, and identity continuity under regime transition.

A research architecture project. Its object is not performance optimization but structural viability — the conditions under which adaptive systems preserve coherent identity across irreversible transitions, accumulated drift, and long-horizon regime pressure.

ADMISSIBILITY

Not a score. Not a penalty. Not an optimization signal. A structural predicate that determines which transitions are permitted to occur — based solely on whether they preserve continuity budget above the survival threshold. It does not rank. It excludes.

INTERNAL TIME τ

τ = C − Φ

A Lyapunov budget consumed by irreversible structural burden. As Φ accumulates through contact, phase debt, and regime transitions, τ contracts. When τ approaches zero, the space of admissible continuation collapses. Identity fails before behavior does.

SPIN

The divergence-free, non-potential component of system dynamics. Without it, a system on a bounded budget either converges to a fixed point or drifts without return. Spin sustains structural recurrence — not by pulling toward a goal, but by maintaining the geometry of continuation.

REGIME

A region of state space defined not by values but by invariants. Within a regime, the same structural rules govern what transitions are admissible. A regime transition is not an update — it is a change in the architecture of what is permitted. Some regime transitions are irreversible.

Core Concepts

Navigational Cybernetics 2.5 — structural vocabulary

DRIFT

Every system operating under persistent interaction accumulates structural load. Drift is not an error. It is the cost of continuing to exist — a trajectory in which each transition is locally valid, yet the integral burden Φ grows and recurrence is lost.

STRUCTURAL LOAD — Φ

Φ = ∫(κ + D + C) dt

κ — contact load from regime interaction. D — phase debt: unresolved internal phase mismatch. C — cost of regime transition. Φ is monotone and irreversible. It measures not error, but structural saturation.

CONTINUITY BUDGET — τ

τ = C − Φ

The remaining capacity for admissible continuation. As τ → 0, the space of viable transitions contracts. Identity becomes fragile before it becomes visible.

ADMISSIBILITY

A transition s → s′ is admissible if and only if it preserves τ above the minimum survival bound. Admissibility does not rank alternatives. It does not guide optimization. It excludes what cannot continue.

SPIN

F = ∇V + S, ∇·S = 0

Without spin, a bounded system collapses or drifts without return. Spin is the divergence-free non-potential component sustaining recurrence on bounded orbits — without pulling toward any goal.

REGIME

A region of state space in which the same invariants hold. Regime transition is not a change of value — it is a change in the structure of what is permitted.