Recursive Manifold Coherence: A Geometric Framework for Deadtime Recovery in Distributed Trigger Systems

TL;DR

The paper tackles deadtime and pile-up in large distributed detectors by replacing traditional binary coincidence triggers with Recursive Manifold Coherence (RMC), a geometry-informed, low-dimensional coherence state updated in real time. RMC maintains a minimal coherence state $\mathbf{x}[k]$ via a recurrence $\mathbf{x}[k] = \mathbf{A}\mathbf{x}[k-1] + \mathbf{B}\mathbf{u}[k]$, with $\mathbf{A} = \rho \mathbf{I}$ to realize exponential memory, and computes a trigger score $\mathcal{G}[k] = \phi(\mathbf{x}[k])$ evaluated against a threshold $\Gamma$. Distances in parameter space are defined by an information-based metric $d\Theta^2 = G_{ij}(\theta) d\theta^i d\theta^j$, enabling statistically meaningful coherence assessment despite missing observations $\mathbf{u}[k]$ during deadtime. The framework is detector-agnostic, operates on compact feature vectors with explicit liveness tagging, and is suitable for fixed-point FPGA or CPU/GPU implementation, providing improved robustness against data fragmentation and higher resilience to deadtime than conventional coincidence logic. Overall, RMC offers a practical pathway to deadtime-aware triggering in next-generation distributed observatories by converting information loss into controlled uncertainty growth and preserving partially obscured coherence for high-multiplicity events.

Abstract

Large-scale neutrino observatories operate under unavoidable detector deadtime and signal pile-up, leading to systematic inefficiencies in conventional coincidence-based trigger systems. Such triggers typically rely on binary temporal windows and assume continuous sensor availability, causing partial or complete loss of correlated signal information during non-live intervals. We introduce Recursive Manifold Coherence (RMC), a geometric framework that reformulates distributed trigger logic as a continuous state estimation problem in a low-dimensional information space defined by correlated charge and timing observables. Instead of applying hard vetoes during deadtime, the proposed method employs a recursive update rule that propagates a coherence state across sensor nodes, allowing partially obscured signals to be retained and evaluated consistently. Using simulation studies representative of large optical detector arrays, we demonstrate that RMC successfully recovers event-level coherence for high-multiplicity topologies even when direct coincidence chains are broken. By treating the detector response as a smooth manifold rather than discrete hits, the framework achieves superior robustness against data fragmentation compared to standard binary logic. The framework is detector-agnostic and compatible with software-defined trigger pipelines, providing a flexible foundation for deadtime-aware analysis and triggering strategies in future distributed detector systems.

Figures (6)

• Figure 1: Deadtime-bridging visualization. (A) Nominal operation without deadtime: baseline coincidence logic and RMC track the underlying truth. (B) Deadtime overlapping the signal peak: baseline coincidence collapses, while RMC propagates a coherence estimate with controlled decay across the non-live interval and re-locks when observations resume. Shaded region indicates detector deadtime.
• Figure 2: Feature-space geometry induced by RMC weighting. (A) Live observations in the raw charge--timing feature space. (B) Effective geometry after deadtime-aware RMC weighting, where statistically consistent signal-like structure is enhanced while background and deadtime-removed observations are suppressed. Distances reflect statistical distinguishability rather than physical separation.
• Figure 3: Evolution of the RMC coherence state and associated uncertainty. During detector deadtime (shaded region), validated input is suppressed and the state propagates according to the recursive update law, exhibiting controlled decay and uncertainty growth. When observations resume, the state rapidly re-locks to the underlying trajectory.
• Figure 4: Integration of Recursive Manifold Coherence into a streaming trigger pipeline. RMC operates on compact charge and timing features with explicit liveness tagging, enabling deadtime-aware coherence estimation without buffering raw waveforms. The recursive state update runs at fixed cost per sample and feeds a trigger decision based on a scalar coherence score.
• Figure 5: Event recovery efficiency as a function of deadtime probability for different persistence parameters $\rho$. RMC remains stable across a wide range of $\rho$ values, while baseline coincidence logic rapidly degrades.

Theorems & Definitions (1)

• Remark 2.1: Deadtime bridging by state propagation