ARTI geometry of reasoning

We show that different reasoning types leave distinct geometric signatures in transformer embedding spaces, detectable by a lightweight classifier with only 20K parameters. Our Active Reasoning Type Identifier (ARTI) classifies 10 reasoning types at 84.2% accuracy (8.4× chance) from embedding geometry alone — no access to input text. Building on this, we introduce ARTI-routed scoring, a mechanism that soft-blends cosine similarity and direct classification via frozen ARTI type probabilities, achieving StrategyQA 81.0% (+32.6pp over baseline) — the first non-math benchmark with genuine learning in the Continuous Operator Factorized Reasoning Network (CO-FRN) architecture while preserving GSM8K at 48.1%. Key results: • ARTI ensemble: 84.2% accuracy on 10 reasoning types (8.4× chance) • ARTI-routed scoring: StrategyQA 81.0% (+32.6pp), first non-math breakthrough • Pre-factorization embeddings retain 3.5× more type signal than post-factorization (76.7% vs 21.9%) • Three-experiment falsification chain (E16–E18): frozen encoder is structurally necessary • GCMC manifold geometry validation: D_eff ρ = −0.624, center alignment ρ = 0.685, combined R² = 0.678 We further discover that pre-factorization embeddings retain 3.5× more type-discriminative signal than post-factorization features (76.7% vs 21.9%), revealing a fundamental tension in factorization-based reasoning architectures. A three-experiment falsification chain (E16–E17–E18) establishes that the frozen encoder is structurally necessary: any unfreezing of a shared transformer destabilizes the answer embedding space for generic-label scoring. Quantitative validation against the GCMC framework from computational neuroscience confirms that the same geometric properties predicting task-efficiency in biological neural manifolds also predict ARTI accuracy (R² = 0.678). This repository contains the complete manuscript (v2.7, final), experiment code for 20 experiments (E5–E19), shared modules (~4,900 lines of code), and all results (JSON + figures). Model weights (.pt) are excluded due to size but can be regenerated from the provided scripts. All experiments use 3-seed evaluation on full test sets (N = 203–1,603).