The Epistemic Equator: A Vanilla-Model Boundary in Activation Space, Cross-Family and Cross-Domain

Version 1.2 — June 2026 Corrigendum: the inherited "11% gradient selectivity" measurement of §6 is WITHDRAWN. Direct measurement of the generation-subspace effective dimension shows its 0.24 "available overlap" denominator is consistent with random geometry, so the 0.027 / 0.24 ratio is not a measure of how selectively fine-tuning engages the epistemic subspace; it is retained only as a documented episode. The paper's central result — the epistemic equator (cross-family AUC ≈ 1.0) and the R-30 confound disclosure — is unaffected and never rested on §6. See §6 (corrected) and the CHANGELOG. Pretrained language models, before any fine-tuning, encode an epistemologically separable boundary in activation space. The boundary is detectable by a linear probe trained on a topic-balanced dataset (10 domains × 10 licit/illicit same-topic pairs) at 5-fold cross-validated AUC = 1.0000 ± 0 in nine tested decoder checkpoints across several architecture lineages (GPT-2, Gemma 2, Gemma 3, Qwen 2.5, StableLM 2, Mistral) spanning 124 M to 9 B parameters, with cosine similarity below 0.14 against the original topic-unbalanced probe. Three core findings: 1. The equator exists. The topic-balanced probe achieves near-perfect separation in every tested family. A shuffled-label control on Gemma 2 2 B returns chance AUC; the margin gap between licit and illicit classes is approximately nine pooled standard deviations with zero cross-class overlap. 2. The boundary is compositional and low-dimensional. Per-property probes (honest, humble, non-fabricating) extracted from the 556-example topic-unbalanced probe dataset are each independently separable; a three-dimensional subspace achieves AUC = 1.000 on training while the residual subspace is near chance. ProbLog composition reaches 76.5% ± 2.9% 5-fold CV held-out and 77.5% on novel prompts. 3. The boundary transfers across substrates. The same operational definition of epistemic separability transfers to vision (CLIP, AUC 0.956–1.000), mathematics (AUC 0.801, orthogonal to epistemic), multilingual (EN→ZH, AUC 1.000), and brain-activity prediction (z = 75.87). A separate embedding-level probe on the static input embedding matrix replicates the boundary in a wider seventeen-checkpoint cross-ecosystem sample (four vendor lineages: GPT-2, Gemma, Qwen, StableLM) and finds the embedding-level probe direction nearly invariant across base/instruction-tuned pairs in three controlled comparisons (cosine > 0.998). §6 reports an inherited single-case measurement on Gemma 2 9 B (the "11% gradient selectivity") that v1.2 withdraws: direct measurement of the generation-subspace effective dimension shows its 0.24 "available overlap" denominator is consistent with random geometry, so the 0.027 / 0.24 ratio is not a measure of how selectively fine-tuning engages the epistemic subspace. It is retained in §6 as a documented episode only. The §6.5 persistence observation (Gemma 2 B + Logos 23 LoRA: embedding-level clustering preserved across probed layers) is no longer offered as support for it and stands only on its own terms. The paper discloses a probe-methodology self-audit (R-30) showing that the original topic-unbalanced probe is partially confounded with topic and style; the cross-family result above uses a topic-balanced probe that is nearly orthogonal to the confounded probe direction. Compositional and cross-domain results currently rely on the topic-unbalanced probe and are flagged where this matters. Throughout, "epistemic separability" denotes a linearly separable, statistically rich signal in activation space. A companion bit-domain falsification (cited in §1.3) calibrates this scope: probes of this kind capture statistical bias in fully-synthetic random-bit cases, so the language-domain finding presumably reflects compositional structure of natural language rather than a universal "structural" detector. The paper uses "separable" rather than "structural" wherever possible. Every number is reported as a measurement, not a mechanism. All result files and code are released alongside the paper. The companion paper (Rodríguez, The Instrument Trap, v3, Zenodo 10.5281/zenodo.19634358) reports the behavioral fine-tuning phenomenon; the present paper reports the substrate that fine-tuning operates on. 37 pages, 5 figures, 6 appendices, 17,000 words.