Universal Dimensional Scaling in Information-Geometric Rendering: Substrate-Independent Metric Conservation Across Holographic, Biological, and Engineered Manifolds
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.
We 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.
Finally, 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.
Related
- Information coding strategies in biological reservoir computing for multiclass time-series classification
- Building from biodiversity assessment to place-based conservation action across scales of information and governance.
- Development of approaches to documenting information on plant genetic resource accessions as a basis for their guaranteed conservation and effective use
- Integrating complementary biological information for multi-objective enzyme engineering
- Hybrid spatial organization and evidence for magnitude-independent neural coding of linguistic information during sentence production
BibTeX
@misc{abella2026universal,
title = {{Universal Dimensional Scaling in Information-Geometric Rendering: Substrate-Independent Metric Conservation Across Holographic, Biological, and Engineered Manifolds}},
author = {Daniel Abella},
howpublished = {PsyArXiv},
year = {2026},
month = sep,
doi = {10.31234/osf.io/8deq3_v1},
url = {https://osf.io/preprints/psyarxiv/8deq3_v1/},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Universal Dimensional Scaling in Information-Geometric Rendering: Substrate-Independent Metric Conservation Across Holographic, Biological, and Engineered Manifolds
AU - Daniel Abella
PY - 2026
DA - 2026/09/09
PB - PsyArXiv
DO - 10.31234/osf.io/8deq3_v1
UR - https://osf.io/preprints/psyarxiv/8deq3_v1/
AB - 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. We 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. Finally, 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.
ER -