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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
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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
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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
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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
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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.
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
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UNNS Substrate Research Program · Foundation Document · 2026
Universal Admissibility:
The Structural Law
Beneath Physical Reality
A Cross-Domain Synthesis of Persistence, Boundary Behavior,
Operator-Selective Response, and the Geometry of Structural Admissibility
There exists a universal structural law that decides which ordered relational configurations can persist as stable observables — and it sits logically prior to dynamics, symmetry, or chance. This is the central claim of the UNNS Substrate programme, now fully formalised in a 62-page foundation document.