A φ-Parameterized Bounded Phase Gate for Structured Residual Modulation Ablation-Ready Research Scaffold for the TULLY / Ly-Algebra Lineage
Abstract
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
18th October 2026
---
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.
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BibTeX
@misc{tully2026φparameterized,
title = {{A φ-Parameterized Bounded Phase Gate for Structured Residual Modulation Ablation-Ready Research Scaffold for the TULLY / Ly-Algebra Lineage}},
author = {Chloe Tully},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23444864},
url = {https://zenodo.org/records/23444864},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A φ-Parameterized Bounded Phase Gate for Structured Residual Modulation Ablation-Ready Research Scaffold for the TULLY / Ly-Algebra Lineage
AU - Chloe Tully
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23444864
UR - https://zenodo.org/records/23444864
AB - 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 [email protected] 18th October 2026 --- 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.
ER -