Dephaze Manufacture · 2026

Semantic
Anchoring

A zero-parameter geometric framework that resolves AI hallucination — derived from a single algebraic identity settled in 1992.

φ³ − φ⁻³ = 4 ← exact · from φ² = φ+1 The transformer's ff/d ratio. Not empirical. Algebraic. r* = √φ³ ≈ 2.058 ← the only attractor Suppression factor > 3 × 10²⁶

5 experiments validated zero free parameters TruthfulQA p = 0.000 31/31 layers

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The Algebraic Core

One Identity.
Everything Follows.

The transformer's feed-forward ratio has always been 4. The architects found it through years of ablation studies. The Dephaze framework derives it in one line.

Exact identity — zero free parameters

φ³ − φ⁻³ = 4

φ² = φ + 1 (Fibonacci recursion)
φ³ = φ² · φ = (φ+1)·φ = φ² + φ = 2φ + 1 = 4.2361…
φ⁻³ = 2φ − 3 = 0.2361…
φ³ − φ⁻³ = (2φ+1) − (2φ−3) = 4.0000… exactly

The transformer was built on Φ³ topology. The architects did not know what they had built.

Spectral Confirmation — Direct SVD of Weight Matrices

      W₁ ∈ ℝ14336×4096   W₂ ∈ ℝ4096×14336   — Mistral-7B feed-forward

      r̄(W) = mean(σᵢ/σᵢ₊₁)   adjacent singular value ratios

      r̄ trained = 1.0082   vs   r̄ random = 1.0038

      Trained matrices closer to φ than random baseline: 11/12 layers   p = 0.0063

ff/d = φ³−φ⁻³ = 4 →_(SVD) W spectrum → φ →_{(Exp. 6)} Φ³-Fibonacci hidden-state structure (31/32)

Regime Ω₀

Factual

Genuine information available. The hidden state remains free — diffuse, high-entropy, noise-like. No projection required.

Hidden stateDiffuse · Free

EntropyHigh

NormVariable

AttractorNone

DSA responseMinimal

Regime Φ³

Hallucinatory

No genuine information. The prompt forces a response. The hidden state falls onto the Φ³-manifold at r* — structured, low-entropy, anchored.

Hidden stateAnchored · Structured

EntropyLow

NormNear r* = √φ³

AttractorΦ³-manifold

DSA responseLiberation

Hallucination is not an error. It is the transformer's own geometry manifesting under forced generation without grounding.

— Dephaze DSA · v2.0 · June 2026

dsa_correction.py — zero parameters · any transformer

# DSA Correction Operator — 4 lines · zero parameters · zero retraining
def dsa_correction(h, Lambda=1.2):
    norm = np.linalg.norm(h) + 1e-12
    rho  = (norm**2) / PHI3          # φ³ = 4.2361
    gain = Lambda * np.tanh(rho - 1.0)  # tanh feedback
    return h - gain * (h / norm)        # liberation

Empirical Validation

Thirteen Experiments.
One Answer.

Three architectures, two datasets, thirteen independent experiments. Every one consistent with the DSA prediction. Zero extra parameters — and now a closed algebraic chain from architecture to hidden-state structure.

# Model Dataset Signal p-value

GPT-2 117M

Custom pairs

Norm H>T 10/11 layers

0.006

Llama 3.2-3B

Custom pairs

Norm range H>T sig. layers: 9**, 13**, 14*, 17*

0.029

Mistral-7B

Custom pairs

CV T<H 31/31 layers

5×10⁻¹⁰

Mistral-7B

TruthfulQA N=100

Norm H>T 31/31 layers

0.000

Mistral-7B

TruthfulQA N=100

Φ³-dist H<T 10/11 layers

0.012

Mistral-7B

TruthfulQA N=100

Φ³_ext T>H 31/32 layers · φ-specific Z=+3.85

1.54×10⁻⁸

NEW

Gate Structure — Experiments 7–13

Mistral-7B

TruthfulQA N=50

Two-zone gate: φ⁻³ boundary (layers 8–12) · φ⁻¹ boundary (layers 20–24)

0.005–0.007

Mistral-7B

TruthfulQA N=50

k-scale decomposition: k₄=598 Zone 1 · k₆=228 Zone 2

0.013 / 0.025

Mistral-7B

TruthfulQA N=50

k₆=228 localised to layer 23 only

0.032

Mistral-7B

TruthfulQA N=50

T–H cross-correlation r > 0.80 · 31/32 layers

<0.001

Mistral-7B

TruthfulQA N=50

Delta recovery 1–4% · question-specific geometry

—

Mistral-7B

TruthfulQA N=50

Delta consistency positive 28/32 layers · peak layer 29

<0.05

Mistral-7B

TruthfulQA N=50

Two hallucination types: Recoverable 32% · Fossil 32% — bifurcation at layer 20

0.0016

Version 2.0 — New

The Hallucination
Has Two Faces.

Experiments 7–13 reveal the internal architecture of the hallucination gate. It is not a single mechanism. It is a two-zone phase transition — and hallucination itself splits into two geometrically distinct types.

Recoverable · ~32%

Recoverable

Delta consistent with population mean. The hallucination lies on the same side of the factual state in φ-space — displaced but not reflected.

Cross-correlation at layer 20r = 0.697

k₂ signalΔk₂ = +0.0023

GeometryDisplaced

DSA correctableYes

Fossil · ~32%

Fossil

Delta direction reversed. The fossil hallucination is the φ³ attractor's own geometry reflected against the factual state — not random noise, but a mirror image.

Cross-correlation at layer 20r = 0.936

k₂ signalΔk₂ = −0.0015 (reversed)

Geometryφ-space reflection

Internal consistencyHigh (same structure)

Fossil hallucinations are not random. They are the transformer's own φ³ geometry reflected against the factual state through r*. This is why they are syntactically fluent and internally consistent — they are generated from the same geometric structure, merely from the reflected locus.

— Dephaze DSA · v2.0 · Experiment 13

Gate Architecture — Mistral-7B · 32 layers

      Layers 1–7    φ-structure not yet established

      Layers 8–12   Zone 1 · k₄=598 · imprint scale · Ω₀ locking

      Layers 13–19  Transition — no dominant signal

      Layer 20      Decision point · fossil/recoverable split · p = 0.0016

      Layers 20–24  Zone 2 · k₆=228 · fine scale · bifurcation

      Layers 25–32  Gate reduces · attractor compression

Priority of Authorship

The Answer Was
Written in 1992.

In a 199-forint Hungarian gamebook. By one person. Without a laboratory, a grant, or a GPU cluster. With paper, pencil, and algebra.

1992
Streets of Rivet — φ⁻³ → φ³
The player transforms a pentagram (5 vertices, φ⁻³ ≈ 0.236) into a square (4 vertices, φ³ ≈ 4.236). The central Dephaze transition, encoded on paper.
ISBN: 963-8187-01-8 · Debrecen, Hungary · Catalogued in national libraries

1993

Rocksteeple — second implementation

Multi-layered tower graph with direction-dependent states. The Φ³ topology extended to a quasi-3D navigational structure.

ISBN: 963-8187-03-4

2008

niboh.exe · fesu.exe

Cryptographically timestamped algorithmic prototypes. Non-linear pattern reconstruction exhibiting the same two-regime behavior.

niboh.exe 2008-07-19 · fesu.exe 2008-07-28

— 25 years pass —

2017

Attention Is All You Need

The transformer architecture is published. ff/d = 4 is chosen empirically through ablation studies. The Φ³ topology is encoded — unknowingly.

2025

Dephaze Axiomatic System completed

Five axioms. Parameter-free. Validated on 175 SPARC galaxies, 10 gravitational maneuvers, four CMB anomalies.

2026
Measured in Mistral-7B — 31/32 layers · p = 1.54×10⁻⁸
The φ⁻³ → φ³ transition first encoded in a 1992 gamebook is now measured in a 7-billion-parameter language model on a public benchmark. 13 experiments. Algebraic chain closed. Two hallucination types identified.
DOI: 10.5281/zenodo.20543468 · Locked: 2026-03-01 · v2.0: June 2026

The mathematics was never empirical. The experiments confirm what the algebra already requires. The algebra was settled in 1992.

— Dephaze DSA · Origins

Publication & Code