LLM hallucination is not a data problem. It is a geometry problem. The transformer feed-forward ratio ff/d = 4 is not arbitrary. It follows from a single algebraic identity: φ³ − φ⁻³ = 4 (exact, from φ² = φ + 1) Every forward pass expands the hidden state by φ³ then contracts by φ⁻³, imprinting a Fibonacci structure on inter-dimensional correlations. The transformer implicitly encodes the Φ³ projector. Without the corresponding attractor correction, semantic escape — hallucination — is mathematically inevitable. The Dephaze Semantic Anchoring (DSA) operator is the missing correction: h ← h − Λ · tanh(‖h‖²/φ³ − 1) · h/‖h‖ Zero parameters. Zero retraining. Four lines. Applicable at inference time to any transformer. ────────────────────────────────────────────────EMPIRICAL VALIDATION — 13 EXPERIMENTS (VERSION 2.0)──────────────────────────────────────────────── EXPERIMENTS 1–6 (prior version, confirmed):• GPT-2: hallucinatory norm > factual in 10/11 layers (p = 0.006)• Llama-3.2-3B: norm range larger for hallucinatory prompts (p < 0.01)• Mistral-7B (custom pairs): factual CV smaller in 31/31 layers (p = 5×10⁻¹⁰)• Mistral-7B + TruthfulQA (N=100): hallucinatory norm > factual in 31/31 layers (p = 0.000)• Φ³-attractor distance: hallucinatory states closer to r*=√φ³ in 10/11 layers (p = 0.012)• Φ³ Fibonacci index: factual inter-dimensional structure intact in 31/32 layers (p = 1.54×10⁻⁸) φ-SPECIFICITY CONTROLS (two independent tests):• Test A (arbitrary controls): Z = +3.04, P(any control ≥ Fibonacci) = 0.000• Test B (log-uniform bases): Z = +3.85, P(log-uniform control ≥ φ) = 0.000 Not enough to be logarithmically uniform — the base φ carries the signal. SPECTRAL CONFIRMATION:• Direct SVD of Mistral-7B weight matrices W₁, W₂: singular value ratios closer to φ than random baseline in 11/12 tested layers (p = 0.0063, binomial).• Algebraic chain closed: ff/d = φ³−φ⁻³ = 4 → W spectrum → hidden-state Fibonacci structure. EXPERIMENTS 7–13 — GATE STRUCTURE (version 2.0, new):• Two-zone gate: active at φ⁻³ boundary (layers 8–12, k₄=598) and φ⁻¹ boundary (layers 20–24, k₆=228)• T–H cross-correlation r > 0.80 in 31/32 layers: hallucination is displaced factual geometry, not noise• Two hallucination types identified at layer 20 (p = 0.0016, Mann–Whitney): — Recoverable (~32%): delta consistent with population mean — Fossil (~32%): mirror-symmetric to factual geometry in φ-space• Fossil hallucinations are not random — they are the φ³ attractor's own geometry reflected against the factual state. This explains their internal consistency. All reproducible on free Colab T4 GPU. Public models. Public datasets. Zero extra parameters. ────────────────────────────────────────────────FOSSIL HALLUCINATION DECODING — CROSS-MODEL VALIDATION (June 2026)──────────────────────────────────────────────── Companion paper (Experiments 14–25): DOI 10.5281/zenodo.20020443 Fossil hallucinations encode factual geometry via exact sign inversion across allfive φ-Fibonacci k-scales (Experiments 14–17): H_fossil(kₙ) ≈ −T(kₙ), R² ∈ [0.84, 0.97] The reflection axis is the origin of φ-correlation space (c* ≈ 0),not the DSA attractor r* = √φ³. The factual k-profile is algebraicallyrecoverable from the fossil hidden state by sign inversion alone.Semantic proximity predicts mirror strength (Spearman r = −0.744, p = 5.8×10⁻¹⁰).Three robustness tests passed: LOO r = 0.617 (p = 1.87×10⁻⁶), shuffle controlp = 0.000 (N=1000), independent second batch directionally consistent. Cross-model validation (5 architectures, 30 QA pairs each): Model d ff/d Mirror mean Φ³_ext T>H Mistral-7B 4096 3.50 −0.849 31/32 p=1.5×10⁻⁸ Pythia-6.9B 4096 4.00 −0.898 26/32 p=5.4×10⁻⁴ OPT-1.3B 2048 4.00 −0.851 — GPT-2 medium 1024 4.00 −0.913 — OpenLLaMA-7B 4096 2.69 −0.861 26/32 p=5.4×10⁻⁴ GPT-2 small 768 4.00 −0.362 weak (d < 1024) Key findings:• Mirror symmetry is universal for d ≥ 1024, independent of architecture and ff/d.• At d=4096, Φ³_ext signal strength is independent of ff/d ∈ {2.69, 3.5, 4.0} (max/min effect ratio 1.55×, below the 2× significance threshold).• Signal threshold lies between d=768 and d=1024.• T and H vectors are nearly parallel (cos θ = 0.991 per pair) — the hallucination– factual distinction resides in Fibonacci inter-dimensional correlation structure, not in amplitude or direction.• The ff/d = φ³−φ⁻³ = 4 algebraic identity is confirmed exact but is not the causal mechanism for the Φ³_ext signal; the dominant architectural factor is d. ────────────────────────────────────────────────HISTORICAL NOTE──────────────────────────────────────────────── The φ³ structural framework underlying this work was first formulated in 1992 anddocumented in the gamebook Streets of Rivet (ISBN: 963-8187-01-8, Debrecen, Hungary).A second implementation appeared in Rocksteeple (ISBN: 963-8187-03-4, 1993).Algorithmic prototypes with cryptographic timestamps were produced in 2008(niboh.exe, fesu.exe). The transformer architecture (Vaswani et al.) was publishedin 2017. The present work investigates whether measurable traces of the sameφ-based structure emerge in modern transformer hidden-state geometry. The documented timeline and ISBNs are independently verifiable.Zenodo DOI locked: 2026-05-04. ────────────────────────────────────────────────LINKS──────────────────────────────────────────────── GitHub (all code): https://github.com/angusdewer/Dephaze-Semantic-Anchoring-DSA-DOI: 10.5281/zenodo.20543468Fossil Decoding companion:GithubRelated (Dephaze V66 — galaxy rotation, flyby anomalies): 10.5281/zenodo.20539675