spectral-topology-preflight

name	spectral-topology-preflight
description	Before dispatching a multi-agent team, run a spectral diagnostic on the proposed communication graph and emit a (ρ, Δ, κ) coordination signature plus a pass/fail verdict against per-task-class thresholds. Builds the row-stochastic operator P from the team graph, computes the successor representation M = (I − γP)⁻¹, and ranks the topology for robustness (κ, condition number), consensus (Δ, spectral gap), and drift (ρ, spectral radius). Per Parks & Alharthi (arxiv 2605.11453), rank order on (κ, Δ, ρ) predicts coordination quality pre-execution with rank correlations of 1.0 / 0.5 / −1.0. Triggers: "dispatch the team", "team topology check", "before running the agents", "is this team configuration OK", "team pre-flight".
user-invocable	true
version	1.0.1
format	"2025-10-02T00:00:00.000Z"
triggers	["team pre-flight","topology check","before dispatching the team","is this team configuration OK","coordination signature"]
updated	"2026-05-16T00:00:00.000Z"
status	ACTIVE
source	arxiv 2605.11453 (Parks & Alharthi), 2605.05657 (RGAO budget algebra)

Spectral Topology Pre-flight

Why

Production multi-agent LLM systems fail at 41-87% rates from coordination defects, not from capability (Nechepurenko & Shuvalov, arxiv 2605.03310). Parks & Alharthi (arxiv 2605.11453) provide the first pre-inference diagnostic: spectral analysis of the team's communication operator predicts robustness (perfect rank correlation r_s = 1.0), consensus (r_s = 0.5), and drift (r_s = −1.0, inverted) before any agent runs. Cheap to compute, large effect on dispatch quality.

How

Given a proposed team graph (agents = nodes, communication paths = edges):

1. Get the signature from the tested implementation — do NOT hand-compute it. The linear algebra (build the row-stochastic operator P, form the successor representation M = (I − γP)⁻¹, and take its eigenvalues / condition number / spectral gap) is already implemented and unit-tested. Call the exported topologySignature(topology, n, gamma) in src/learn/generators/team-generator.ts — pass the topology archetype ('pipeline' | 'leader-worker' | 'mesh' | 'ring' | 'tree' | 'bipartite' | 'critique-route'), the agent count n, and optionally gamma (defaults to 0.9). It returns { rho, delta, kappa, gamma } computed from the closed-form spectra in Parks & Alharthi Appendix A. When you are generating the whole team, generateTeam(...) in the same module produces the signature for you as part of its result. Never estimate or fabricate ρ, Δ, or κ by hand — LLMs cannot reliably invert matrices or compute eigenvalues; always source the numbers from the function.
2. Interpret the three diagnostics returned in the signature:
   • κ (condition number of M) — robustness signal. Lower = more robust.
   • Δ (spectral gap of P) — consensus signal. Larger = faster consensus.
   • ρ (spectral radius of P) — drift signal. Smaller = less drift (inverted from κ).
3. Compare against per-task-class thresholds:
   • For "deep-reason" tasks: prefer small κ, large Δ — robustness matters
   • For "exploration" tasks: prefer larger ρ — drift is exploration, not failure
   • For "consensus" tasks: prefer large Δ above all else
4. Emit the signature — coordination_signature: { rho, delta, kappa, verdict, recommendation? }. Verdict is pass / warn / fail. On fail, recommendation suggests a topology edit (drop/add edge, switch chain↔star↔mesh).