Computational Phase Synchronization

Distributed systems often receive several partial measurements of the same changing process, but those measurements may not arrive in one common cyclic frame. A camera, microphone, inertial sensor, memory module, or artificial agent can preserve useful content while its timing or phase relation differs from that of its peers. Averaging such states before estimating their relative offsets can cancel signal, mix incompatible observations, or create a confident but incorrect fused state. Existing engineering provides several parts of the solution. Hardware synchronization aligns clocks before measurement. Attention and scalar gating weight inputs without necessarily retaining circular relations. Angular synchronization estimates unknown angles from noisy pairwise offsets. Multiscale aperture synthesis imaging demonstrates that distributed optical measurements can retain complex wavefield information, undergo computational relative-phase optimization, and then be coherently fused. Recent artificial systems also use complex activations, phase relationships, recurrent constraint satisfaction, coupled oscillators, or neural synchronization as internal representations. This paper isolates one narrower operation. Each module retains a complex-valued state; a causal estimator compares each module with a reference, tracks the relative offset, rotates states into a common gauge, and fuses them only when held-out validation shows a task benefit. The operation is called computational phase synchronization after the problem and mechanism have been specified. An executable synthetic benchmark tests five declared worlds over 48 seeds each. Adaptive alignment was accepted in every stable-offset and slow-drift-with-jump run. Median normalized mean-squared error fell from 0.014789 to 0.001865 in the stable world and from 0.014854 to 0.002591 in the slow-drift world. The same estimator failed under fast drift, unpredictable offsets, and distractor modules. A validation gate rejected it in every run of those three worlds and reverted to the reference-module baseline. The result therefore supports a conditional engineering claim: explicit phase alignment can help when modules observe a shared state and relative offsets are predictable at the estimator's bandwidth; validation-gated abstention is necessary when those conditions fail. A preregistered semi-synthetic extension then replaced the generated latent trajectory with the analytic signal of a checksum-verified five-minute human ECG record while retaining controlled module offsets, noise, and distractors. Across 48 perturbation seeds per world, selected median NMSE fell from 0.008947 to 0.001173 under stable offsets, from 0.008956 to 0.001327 under slow drift with a jump, and from 0.008955 to 0.002356 in the declared fast-drift condition. The gate rejected every unpredictable-offset and distractor run and returned the reference unchanged. Together, the benchmarks validate estimator and failure-test logic in declared synthetic and semi-synthetic data-generating processes. They do not establish a general AI-task advantage, a clinical result, a biological neural-phase mechanism, Neural Array Projection Oscillation Tomography, Phase Wave Differentials, Self Aware Networks, or consciousness.