{
  "abstract": "A φ-Parameterized Bounded Phase Gate for Structured Residual Modulation\n\nAblation-Ready Research Scaffold for the TULLY / Ly-Algebra Lineage\n\nC. J Tully\n\nIndependent Researcher Engineer\n\nTamworth NSW Australia 2340\n\nhttps://orcid.org/0009-0007-5661-7332\n\nchloetully5@gmail.com\n\n18th October 2026\n\n---\n\nAbstract\n\nWe 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Chloe Tully",
      "orcid": "0009-0007-5661-7332"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9z6ptrj1mfcsr.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23444864",
  "fulltext_url": null,
  "id": "9z6ptrj1mfcsr",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23444864",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9z6ptrj1mfcsr.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:20:48Z",
      "native_id": "23444864",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23444864"
    }
  ],
  "subjects": [],
  "title": "A φ-Parameterized Bounded Phase Gate for Structured Residual Modulation Ablation-Ready Research Scaffold for the TULLY / Ly-Algebra Lineage",
  "title_text": "A φ-Parameterized Bounded Phase Gate for Structured Residual Modulation Ablation-Ready Research Scaffold for the TULLY / Ly-Algebra Lineage",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:48Z",
  "url": "https://research.draconitic.com/paper/9z6ptrj1mfcsr",
  "venue": "Zenodo",
  "versions": []
}