Latent Iteration as Renormalization: Inference-Time Recurrence in a Depth-Recurrent Transformer Flows Attention Geometry Toward the SYK Conformal Fixed Point

Depth-recurrent transformers scale test-time compute by iterating a core block in latent space before emitting tokens. The geometry of these latent trajectories is a named open problem in the latent reasoning literature (survey arXiv:2604.02029, §6.3). We report a pre-registered experiment on Huginn-0125 (arXiv:2502.05171), a 3.5B-parameter depth-recurrent transformer, measuring the per-head attention power-law exponent Δ of the recurrent core at recurrence counts r ∈ {1, 2, 4, 8, 16, 32}. For natural-text inputs the median exponent decreases monotonically with recurrence (Spearman ρ = −0.94), from 0.29 at r=1 to 0.239 at r=32 — converging onto the Sachdev–Ye–Kitaev (SYK) q=4 conformal value Δ = 1/4 — while the count of SYK-near heads grows monotonically (ρ = +0.77). Random-token inputs show an architecture-driven convergence with a transient at Δ ≈ 1/2 (the q=2 prethermal plateau previously observed in training time) but no monotone SYK-near growth. A randomized-weights control freezes completely: Δ_med constant to the sixth decimal across all r, zero SYK-near heads. Inference-time recurrence therefore acts as renormalization-group flow toward the conformal fixed point, and the flow is a property of the trained model, not the iteration procedure. Together with prior results on architectural depth (10.5281/zenodo.19225996) and training time, this completes a three-axis triangulation: the conformal fixed point is an attractor of iterative attending. The published orbit/spiral phenomenology of recurrent-depth latent trajectories acquires a candidate theory — the spiral is flow near an infrared fixed point — and the geometric benefit of additional recurrence saturates when the flow arrives, consistent with convergence-based early-exit criteria. All code, pre-registration (commit 702efd95), per-head data, and experiment notes with recorded protocol deviations are in the public repository 3ld0n/attention-geometry.