{
  "abstract": "Spacetime metric distance, cognitive spatial navigation, and sensory coordinate mapping operate under identical substrate-independent rendering laws. Here, we present a unified information-geometric theory demonstrating that holographic bulk space (AdS_{D+1}/CFT_D), biological neural manifolds, and non-holonomic circuit networks function as scale-invariant Renormalization Group (RG) engines governed by a single metric invariant: the Information Density Tensor (D_{μν})—defined as the Population Fisher Information Metric (I_{μν}) normalized by the invariant state-space volume element (\\sqrt{\\det g}). We prove that preserving local information density (\\nabla_k D_{μν} = 0) across discrete coarse-graining steps along the holographic/hierarchical depth axis requires a universal scale expansion operator: r(D) = 2^{1/D}, where D represents the topological dimension of the manifold.\n\nWe validate this framework across three core domains: 1. Dual Neuro-Geometric Manifestations: In the medial entorhinal cortex (MEC), the IDT predicts the discrete module expansion ratio r(2) = \\sqrt{2} \\approx 1.414 observed in 2D open fields (r \\approx 1.42), while predicting a dynamic metric shift to r(1) = 2.000 in 1D constrained tracks to maintain entropic isometry. In the primary visual cortex (V1), we show that cortical magnification (M) is a deterministic Riemannian coordinate transformation (M \\propto 1/\\sqrt{\\det g}) that equalizes information pressure between the spherical retina and planar cortex. 2. Holographic Bulk-Boundary Duality: In AdS_{D+1}/CFT_D spacetimes and MERA tensor networks, r(D) = 2^{1/D} defines the exact volume contraction factor required to preserve boundary entanglement entropy across spatial scales (r(3) = \\sqrt[3]{2} \\approx 1.260). 3. Engineered Networks: Applying the IDT to non-holonomic circuit manifolds via the Fluctuation-Dissipation Theorem maps statistical Fisher metrics directly onto physical impedance tensors (Z_{ij}), restoring coordinate invariance and eliminating parasitic boundary dissipation.\n\nFinally, we leverage the IDT to formulate a quantitative clinical model: framing Alzheimer's disease acceleration as a non-linear geometric phase transition occurring when cellular mortality breaches a critical metric density threshold (D_{actual} < D_{critical}). We outline an in silico computational optimization protocol and an electrophysiological 1D re-analysis pipeline defining explicit decision boundaries (H_0: r(1) \\approx 1.414 vs. H_1: r(1) = 2.000) to establish empirical falsification criteria.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Abella"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3pcvhd5j9f61j.bib",
  "cited_by": 0,
  "doi": "10.31234/osf.io/8deq3_v1",
  "fulltext_url": null,
  "id": "3pcvhd5j9f61j",
  "issns": [],
  "landing_url": "https://osf.io/preprints/psyarxiv/8deq3_v1/",
  "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": [
    [
      "bepress",
      "Cognitive Neuroscience"
    ],
    [
      "bepress",
      "Neuroscience"
    ],
    [
      "openalex",
      "3109|Complex Systems and Dynamics"
    ]
  ],
  "openalex": "W7212223194",
  "pdf_url": "https://osf.io/8deq3/download",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3pcvhd5j9f61j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:30Z",
      "native_id": "8deq3",
      "source": "osf",
      "url": "https://osf.io/preprints/psyarxiv/8deq3_v1/"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "bepress:Cognitive Neuroscience",
      "subfield": "neuroscience"
    }
  ],
  "title": "Universal Dimensional Scaling in Information-Geometric Rendering: Substrate-Independent Metric Conservation Across Holographic, Biological, and Engineered Manifolds",
  "title_text": "Universal Dimensional Scaling in Information-Geometric Rendering: Substrate-Independent Metric Conservation Across Holographic, Biological, and Engineered Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:30Z",
  "url": "https://research.draconitic.com/paper/3pcvhd5j9f61j",
  "venue": "PsyArXiv",
  "versions": []
}