From the Sophimatics Framework to a Complex-Time Multi-Agent System for Neural–Symbolic Cognitive Analysis

This paper reports the Sophimatic Multi-Agent System (MAS), the first integrated operational implementation of the six-phase Sophimatics framework: a three-tier containerised prototype (React/FastAPI/MySQL, ~25,000 lines of code) with an agent catalog of 1300+ Digital Twin-inspired LLM personas, a three-mode selection architecture, and per-agent weight disclosure. The pipeline executes the six Sophimatics phases, including STℂNN complex-time processing (T = treal + i timag∈ ℂ), whose instance here is untrained and excluded from empirical claims, and human-in-the-loop feedback bounded at three iterations. Agents are selected automatically by a five-step expertise-vector rule, manually via a hierarchical picker, or semi-automatically via slot-based proposals. Two instrumentation indices are reported: the Lexical Grounding Index τ (fraction of response tokens whose stems occur in the source documents) and, as an internal diagnostic of the feedback loop, the Feedback Alignment Index A. Three single-session use cases on public corpora are reported (Zoom and Coca-Cola 10-Ks, GDPR). Mean τ is 0.73 and mean A is 0.80. Expert ratings differ from single-agent baselines by +2.2 to +2.8 points on quality and +4.2 to +4.3 on coverage metrics; both raters were affiliated with the authors’ research group. The protocol for the validation of the grounding index against human judgement is specified in full, with its conditions, sample size and decision criteria, so that it is testable ahead of that work. A compute-matched and random-agent comparison over 27 sessions separates the observed difference into a component attributable to heterogeneous personas and one attributable to expertise-based selection. Measured end-to-end latency scales close to linearly with the number of activated agents, with a small fixed per-session overhead (R2 = 0.996 for a two-parameter fit against N = 1–16). Together, the empirical use cases document the end-to-end operation of the pipeline, while the specified protocols define the controlled validation that remains to be carried out. The current evidence remains preliminary and does not establish general superiority over simpler architectures.