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How Structure Selects Dimension: A Phase Space View of Physical Systems

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Category: UNNS Research
UNNS Substrate Research Program · April 2026 · Emergent Dimensionality

From Margin to Dimension

Mapping structural regimes across 35 physical systems — from atomic spectra to cosmic web surveys — reveals that the number of active dimensions is not a property of space, but a consequence of how structure is allowed to exist.
The central result: dimensionality is not assumed — it is selected by connectivity margin. A single structural parameter, measurable from any ordered physical sequence, determines which degrees of freedom are accessible and which remain suppressed.
Read the full manuscript: Emergent Dimensionality in the UNNS Substrate
35 Systems · 4 Domains Cosmic Web · Atomic · Crystallographic · Condensed Matter 10 New Theorems Renormalization-like Flow γ Stratification Zero Hard USL Violations
Corpus: 93 datasets · 22,817 evaluations · 11 physical domains Pipeline: UNNS Dimensional Regime Synthesis v1 Instruments: STRUC-I v1.0.4 · STRUC-PERC-I v2.4.1 · unns_scaling_extractor.py

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One Margin, Four Forces: A Structural Account of Interaction Regimes

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Category: UNNS Research
UNNS Substrate Research Program · April 2026 · Interaction Unification

Where Structural Margin Shapes Physical Interaction

A single structural parameter — the connectivity margin m(L) — classifies all known physical interactions as asymptotic regimes of one invariant. The diversity of forces is not fundamental. It is the structural footprint of proximity to instability.
📄 Manuscript · PDF Interaction Unification in the UNNS Substrate: All Fundamental Forces as Margin-Regulated Structural Regimes ↗
Connectivity Margin m(L) Four-Regime Classification No Fifth Force Higgs: Derived Coupling 93 Datasets · 22,817 Evaluations Maximum-Margin Principle Cross-Domain Micro-Tests
Status: Working Manuscript · April 2026 Corpus: 93 datasets · 11 physical domains Central object: Connectivity margin m(L) Key result: Zero inter-class transitions across 22,817 evaluations

Read more: One Margin, Four Forces: A Structural Account of Interaction Regimes

The Structural Bridge: How a Single Margin Governs Stability, Capacity, and Phase Behavior Across Physical and Computational Systems

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Category: UNNS Research
UNNS Substrate Research Program · April 2026 · Theoretical Unification

One Margin Explains Stability, Capacity, and Change

Connecting Stability, Capacity, and Phase Behavior in the UNNS Substrate — a structural margin reveals why physical systems remain stable under deformation and connects energy-based models, neural networks, and quantum dynamics.
Structural Rigidity · Principle 1 Hopfield Capacity Extension Ising / Spin-Glass Bridge Quantum Annealing 93 Datasets · 22,817 Evaluations Zero Inter-Class Transitions
Status: Working Manuscript · April 2026 Domains: 11 physical domains, atomic to cosmic Central object: Connectivity margin m(L) > 0 Companion: PRP · Dual Observability · Phase Mapping

Read more: The Structural Bridge: How a Single Margin Governs Stability, Capacity, and Phase Behavior Across...

Why Structure Doesn’t Change: Flat Phase Maps and Boundary Regimes in the UNNS Substrate

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Category: UNNS Research
UNNS Substrate Research Program · Phase Mapping · April 2026

The Geometry
That Refuses to Break: Mapping the Regimes of Structure

The first systematic deformation study of realizability structure: 22,817 evaluations across 93 datasets and 11 physical domains reveal a locally rigid, boundary-governed structural observable — and expose representation, not deformation, as the dominant structural variable.
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📄 Manuscript Bounded Structural Rigidity and Representation-Driven Structure — Full Working Manuscript (PDF)
STRUC-PERC-I v2.4.1 93 datasets · 22,817 evaluations Zero inter-class transitions Zero non-trivial commutators 11 physical domains Principle 1 — corpus-supported Field Generator v1.0
Instrument: STRUC-PERC-I v2.4.0/2.4.1 Pipeline: Field Generator (Python + Node.js + Puppeteer) Grid: 17×17 joint (α, μ) · Ω = [0.80, 1.20]² Date: April 2026 · unns.tech

Read more: Why Structure Doesn’t Change: Flat Phase Maps and Boundary Regimes in the UNNS Substrate

The Two Coordinates of Reality

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Category: Labs
UNNS Substrate Research Program · April 2026

A Second Coordinate
of Physical Structure

From Admissibility to Dual Observability
We discovered that physical systems are not one-dimensional.
Every system is defined by two independent structural coordinates: what is allowed to exist — and how it is internally organized.
This breaks a long-standing assumption: that structural validity determines structure itself. Knowing that a system can exist tells you nothing about how it is connected inside. These are different properties. They require different instruments to measure.
Dual Observability · Proved Zero Violations · 5,233 Runs New Structural Layer 14 Domains · Atoms to Galaxies Realizability · Formally Derived Forbidden State · Empirically Confirmed

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