From Timeless Pattern to Dynamic Reality: Deriving the Recognition Length and the Lock–In Mechanism

Recognition Science posits that physical reality crystallises out of a timeless pattern layer (PL) when pairs of potential states form a stable recognition lock. From five axioms—Existence, Dual-Recognition, Minimal Overhead, Self-Similarity, Lock-In—we derive a unique recognition length λrec by equating the one-bit Landauer cost with the entanglement-entropy bound of a minimal causal diamond, without presupposing ℏ or G. A dual-log cost functional proves regulator-independence and fixes the stationary scale at q⋆ = φ/π, while a Regge-calculus minimisation shows that an equilateral face of area √3 λ²rec/4 saturates the bound. Each lock-in releases the universal quantum Elock = χℏc/λrec with χ= φ/π; the cumulative power κElock drives cosmic acceleration through a simple master equation and maps directly onto the observed dark-energy density. Finally, we show that G, ℏ, kB and α emerge as algebraic functions of λrec and χ, eliminating circular dependence and yielding sharp, near-term tests in MICROSCOPE-2 WEP measurements, nanometre-scale Casimir probes and advanced-LIGO propagation lags.