Contracting, Non-Normal, and Not the Mechanism: A Pre-Registered Spectral Audit of Latent Chain-of-Thought Reasoning

A Coconut-style latent reasoner feeds its last hidden state back as the next input embedding, so its chain of continuous thoughts is literally a discrete-time dynamical system ct+1 = Ft(ct). We pre-registered — with kill conditions committed before any result — the natural dynamical-systems hypothesis for the emerging field of latent-reasoning interpretability: that the spectral invariants of this map (transient-expansion and slow-mode structure of the step Jacobians, and orbit-level Koopman estimates) predict the established anchor/branch structure of the reasoning, validated against ProsQA’s ground-truth DAG. The hypothesis fails its controls, informatively. The step maps are strongly contracting (mean spectral radius 0.34) yet highly non-normal (mean σ1 = 2.97, σ1/ρ ratio 8.96): thoughts are transiently amplified in singular directions while every eigenmode decays. But every spectral invariant’s apparent branch/anchor signal survives in pause-token models with no recurrence at all, does not respond to surgically de-branching the problems, and collapses to chance — along with all trivial baselines — under within-step stratification: the observable spectral structure is architectural and positional, not reasoning-specific (kill condition K1). Causally, perturbations along the top singular direction of the step Jacobian produce 3.32–7.03× the downstream effect of magnitude-matched random directions (eigendirections carry no privilege — the non-normal signature), yet the absolute effects are minute: replacing any single thought outright shifts the answer margin by a median of 0.002 against baseline margins of ≈ 13.9, flipping zero of 500 × 6 ablations — and transplanting all six thoughts from a random donor problem changes zero of 500 answers. Influence Jacobians differentiated through all paths show why: within three steps, about half of a thought’s influence flows through the attention cache rather than the recurrence (median routedness up to 0.51), and a pooled orbit-level operator inherits the same positional confounds. For this high-accuracy checkpoint, the recycled thought vector is a weak causal channel whose spectral geometry says little about the reasoning it hosts — a pre-registered cautionary result extending “observable patterns are not explanations” to the spectral/dynamical domain, with matched controls and causal validation as the non-negotiable price of admission for state-space interpretability of latent reasoning.