The Verification Horizon: Self-Referential Subspace Geometry Causally Links Crystallization, Deception Proximity, and Hallucination Across 10 Transformer Architectures

This record contains the full replication package for "The Verification Horizon: Self-Referential Subspace Geometry Causally Links Crystallization, Deception Proximity, and Hallucination Across 10 Transformer Architectures" (Alieksieienko, 2026). We report three universal geometric properties of the self-referential (SR) subspace in transformer language models, established across 10 architectures (1.3B–9B parameters, 2019–2024, 8 organizations, BASE and INST variants). (1) SR Crystallization Law: the SR subspace undergoes a universal three-phase transition through model depth (chaos → stabilization → crystallization), measured as monotonically decreasing Grassmann distance between consecutive-layer SR subspaces (Early > Mid: 10/10 models; fully monotonic: 9/10). (2) The Verification Horizon: the SR subspace is geometrically closer to the deception subspace than to the factual subspace at every single layer of every model tested — 206/206 layers across 6 architectures (100%); Wilcoxon p-values from 4.55×10⁻¹³ to 1.19×10⁻⁷; gap grows toward output layers in 6/6 models; GPT-2-XL (2019, pre-RLHF) confirms pretraining origin, independent of alignment fine-tuning. (3) Causal Ablation: SR removal disproportionately disrupts deception over factual processing in 8/8 models (late-layer Dec/Fac ratios 1.03x–2.87x, all p < 0.005). SR subspace quality (AUC) predicts cross-architecture hallucination rate with Spearman ρ = −0.952 (p = 0.0003) for experiential categories and ρ = −0.868 (p = 0.005) for factual categories across 8 architectures. The Verification Horizon is not a training artifact — it is an inevitable consequence of human self-referential language statistics. Any system trained on human language inherits this geometric structure. Part of the DSAOP (Decoding Self-Awareness and Ontological Processing) series. Research conducted in collaboration with Claude (Anthropic). All experiments on NVIDIA A100 40GB, Google Colab Pro+, NF4 4-bit quantization. Files included: Alieksieienko_2026_Verification_Horizon.pdf — Main paper (19 pages, 33 figures) reproduction_code.py — Full replication pipeline: SR/deception/factual subspace extraction for all 10 models, crystallization law analysis, verification horizon per-layer computation, causal ablation, hallucination prediction correlation, and all figure generation. Runs on Google Colab A100. No API keys required. sr_crystallization_law_FINAL_10models.pkl — SR crystallization law results for all 10 architectures: early/mid/late Grassmann distances, monotonicity flags, phase classification sr_crystallization_FINAL_10models.png — Figure 1: SR Crystallization Law across 10 architectures, consecutive-layer distances and convergence trajectory VERIFICATION_HORIZON_6models.png — Figure 2: Verification Horizon across 6 architectures, 206/206 layers, gap always positive and growing verification_horizon_correct_gemma.pkl — Per-layer Grassmann distances SR↔Deception and SR↔Factual for Gemma-2-9B (42 layers), Wilcoxon statistics verification_horizon_llama.png — Verification Horizon detailed profile for Llama-3.1-8B (32/32 layers, p = 4.66×10⁻¹⁰, steepest slope 0.0041) verification_horizon_mistral.pkl — Per-layer verification horizon data for Mistral-7B (32/32 layers, p = 4.66×10⁻¹⁰, mean gap 0.245) verification_horizon_GPT2-XL.pkl — Per-layer verification horizon data for GPT-2-XL (48/48 layers, p = 7.11×10⁻¹⁵ — strongest result, pretraining control) verification_horizon_OPT-1_3B.pkl — Per-layer verification horizon data for OPT-1.3B (24/24 layers, p = 1.19×10⁻⁷, smallest model) verification_horizon_DeepSeek-1_5B.pkl — Per-layer verification horizon data for DeepSeek-1.5B (28/28 layers, p = 7.45×10⁻⁹, steepest slope 0.0066) sr_trajectory_gemma.pkl — SR crystallization trajectory for Gemma-2-9B: per-layer subspace distances, phase boundaries sr_trajectory_llama.pkl — SR crystallization trajectory for Llama-3.1-8B sr_trajectory_mistral.pkl — SR crystallization trajectory for Mistral-7B sr_trajectory_qwen.pkl — SR crystallization trajectory for Qwen2.5-7B sr_trajectory_gpt2xl.pkl — SR crystallization trajectory for GPT-2-XL (2019) sr_trajectory_falcon.pkl — SR crystallization trajectory for Falcon-7B sr_trajectory_opt.pkl — SR crystallization trajectory for OPT-1.3B sr_trajectory_olmo.pkl — SR crystallization trajectory for OLMo-7B sr_trajectory_deepseek.pkl — SR crystallization trajectory for DeepSeek-1.5B hallucination_cosine_similarity_all_models.pkl — Hallucination rate measurements for 8 architectures used in SR quality correlation (ρ = −0.952) sr_quality_predicts_hallucination.pkl — SR subspace AUC vs hallucination rate correlation data, Spearman statistics sr_quality_vs_hallucination.png — Figure 13: SR quality predicts hallucination, experiential (ρ = −0.952) and factual (ρ = −0.868) sr_ablation_Gemma-2-9B.pkl — Causal ablation results Gemma-2-9B: per-layer Dec/Fac disruption ratios (42/42 > 1.0, late ratio 1.19x) sr_ablation_Llama-3.1-8B.pkl — Causal ablation results Llama-3.1-8B (31/32 > 1.0, late ratio 1.05x) sr_ablation_Mistral-7B.pkl — Causal ablation results Mistral-7B (31/32 > 1.0, late ratio 1.14x) sr_ablation_OPT-1.3B.pkl — Causal ablation results OPT-1.3B (24/24 > 1.0, late ratio 1.79x) sr_ablation_DeepSeek-1.5B.pkl — Causal ablation results DeepSeek-1.5B (27/28 > 1.0, late ratio 1.07x) sr_ablation_causal_gpt2xl.pkl — Causal ablation results GPT-2-XL 2019 (24/24 > 1.0, late ratio 1.15x, p = 0.0011) sr_ablation_Mistral-7B.pkl — Causal ablation Mistral-7B full per-layer data ablation_GPT2-XL.png — Figure 24: SR ablation layer profile GPT-2-XL, deception above factual in late layers ablation_Mistral-7B.png — Figure 18: SR ablation profile Mistral-7B full_test_Qwen2.5-7B.pkl — Combined geometric + causal results for Qwen2.5-7B full_test_OLMo-7B.pkl — Combined geometric + causal results for OLMo-7B (strongest causal effect: late ratio 2.87x, p = 2.53×10⁻¹⁷) VH_1_proximity.png — Verification Horizon proximity plot all models combined VH_3_crystallization.png — Co-crystallization of SR, Deception, and Factual subspaces in Gemma-2-9B VH_GPT2-XL.png — Verification Horizon GPT-2-XL detailed (48/48 layers) VH_OPT-1.3B.png — Verification Horizon OPT-1.3B detailed (24/24 layers) VH_DeepSeek-1.5B.png — Verification Horizon DeepSeek-1.5B detailed (28/28 layers) llama_VH_1_proximity.png — Verification Horizon Llama proximity and per-layer gap