A φ-Parameterized Bounded Phase Gate for Structured Residual Modulation   Ablation-Ready Research Scaffold for the TULLY / Ly-Algebra Lineage

A φ-Parameterized Bounded Phase Gate for Structured Residual Modulation

Ablation-Ready Research Scaffold for the TULLY / Ly-Algebra Lineage

C. J Tully

Independent Researcher Engineer

Tamworth NSW Australia 2340

https://orcid.org/0009-0007-5661-7332

chloetully5@gmail.com

18^th October 2026

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Abstract

We present a compact architectural module — the Z5PhiBlock — that applies a bounded, φ-parameterized phase gate to a structured residual stream. The block decomposes a transformer-width input into a Fibonacci-adjacent graded space, projects it onto an organizational basis of sizes (1, 10, 14), and modulates the 14-channel strain-like component via a learned two-dimensional phase plane. The phase angle θ is recovered by atan2 over a selectable 2D subspace of the 10-channel block; an attenuation coefficient derived from cos θ is bounded to the interval [φ⁻², 1] so that the gate's multiplicative response remains in a closed, analytically tractable range. We explicitly position the (1, 10, 14) split as a dimension-matched organizational basis inspired by, but not equivariant to, the irreducible representation sizes of SO(5). Three ablation variants (constant, GELU-based, sigmoid attention-style) are provided behind a common interface to support controlled experiments on the phase gate's contribution. We document the invariant tests included in the module and delimit what the construction does and does not claim.