Quantum Coherence as Gated Recognition: An Eight-Tick Mechanism with Parameter-Free Bridges
Recognition Physics Institute
Summary
This paper frames quantum coherence as an operational property of a discrete recognition process governed by exact eight‑tick window identities. These identities act as a matched filter that preserves phase aligned to the eight‑tick schedule while canceling misaligned components. A uniquely characterized convex cost on positive reals underpins a path‑weight construction that yields Born weighting and, via permutation invariance, the BE/FD exchange classes. The work provides auditable predictions including window‑8 equalities, a matched‑filter coherence theorem with a phase‑drift bound, multi‑probe scaling laws, discrete‑lag cosines with a stretched‑exponential envelope, and a units K‑gate consistency check.
Abstract
We address the core question of quantum coherence: when is phase information preserved and when does it dephase under realistic readout? We show that coherence is an operational property of a discrete recognition process obeying exact eight-tick window identities. These identities provide necessary and sufficient conditions for phase preservation over aligned windows and act as a matched filter that retains only structure aligned to the eight-tick schedule while canceling everything else.
Quantitatively, a unique convex, multiplicatively symmetric cost on $\mathbb{R}_{>0}$, $J(x) = \tfrac{1}{2}(x + x^{-1}) - 1$ (equivalently $J(e^t)=\cosh t - 1$), is characterized by symmetry, unit normalization, and a Jensen-type averaging principle on the log axis. From $J$ we build a path weight that yields the Born rule (modulus) and, via permutation invariance, the BE/FD exchange classes. Together with atomicity and exactness (discrete $w=\nabla\phi$), the eight-tick schedule stabilizes coarse phase and quantifies when interference survives averaging.
We give operational audits and predictions: (i) exact window-8 sum/average equalities; (ii) a matched-filter coherence theorem with a phase-drift bound; (iii) multi-probe scaling laws (logarithmic extension of visible coherence time), (iv) discrete-lag cosines with a stretched-exponential envelope, and (v) a units K-gate consistency check for display ratios. All statements are presented in classical notation and are accompanied by mechanized witnesses (Lean) and a minimal audit manifest.
Key Points
- Eight‑tick matched filter: Exact window identities preserve aligned phase and cancel misaligned structure.
- Unique convex cost: $J(x)=\tfrac12(x+x^{-1})-1$ under symmetry and averaging yields Born weighting.
- Exchange statistics: Permutation invariance recovers BE/FD classes within the recognition framework.
- Operational audits: Window‑8 equalities, phase‑drift bound, multi‑probe scaling laws, discrete‑lag cosines.
- Units bridge: K‑gate consistency check aligns time/length displays without hidden parameters.