Constructive Accessibility from Committed Prefixes in Random 3-SAT: A Kinetic Transition in Reachable Future Under Forward Irreversible Construction

Classical random-SAT phase diagrams begin from the set of completed satisfying assignments. One- way construction begins earlier: from a committed prefix and the satisfying futures still reachable from it. We study that prefix-space object directly. For a specified forward, non-backtracking process on random 3-SAT, we measure a constructive accessibility transition (CAT): the probability of reaching any satisfying completion drops sharply at αcross(1000) = 1.5352 (bootstrap 95% CI [1.526, 1.555]), well below the clustering transition (αd ≈ 3.86) and far below the widely cited satisfiability threshold region near αc ≈ 4.267. Across nine system sizes (n = 20 to 1000), midpoint drift decelerates strongly; an out-of-sample finite-asymptote fit through n ≤ 700 predicts αcross(1000) ≈ 1.541, within 0.006 of the densified observation, whereas drift-to-zero alternatives miss by about 0.27. Together these results support a finite, process-indexed boundary rather than ordinary finite-size drift on the tested scales.

The paper contributes not only a boundary location but a resolved empirical fingerprint of constructive accessibility. Failures are overwhelmingly end-loaded, with jam risk concentrated in the final ∼ 1–2% of construction; near the crossing, most outcome variance is within-instance rather than between-instance, consistent with pathwise competition on typical formulas; and coarse local diagnostics remain only weakly predictive until deep into construction. In the exact-coverage bridge/backtrack zone, a CDCL bridge check confirms that all 194 tested jam prefixes at n = 1000 and α ∈ {1.53, 1.55} are residual UNSAT under the exact realized commitments, with no SAT cases and no timeouts. Bounded rewind then shows that this non-extendability is often deep on the tested scale: undoing one or two assignments never restores SAT, and about 70% of jammed prefixes remain non-extendable even after rewinding 50 assignments. A matched robustness sweep at n = 1000 then shows that the early collapse survives pool-size changes and exact-all-local move exposure, with crossings remaining in the same broad 1.53–1.55 band and with the late-jam signature preserved.

The quantity that collapses here is not satisfiability itself but reachable future under forward irreversible commitment. Near the boundary, the relevant state is the formula together with its committed history, because the same instance can host successful, shallowly recoverable, and deep- trap trajectories. Random 3-SAT therefore serves here as the first resolved measurement site for constructive accessibility from committed prefixes, complementing rather than replacing the classical endpoint-focused phase picture.