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

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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 ↗
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

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

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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
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

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

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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.
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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

Structural Regime Theory and the Universal Admissibility Framework

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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

Instrument: STRUC-I v1.0.4
Corpus: >1,500 ladders · >150,000 assessments
Constants: α · μ · αₛ · αG
Domains: 10 physical + biological
Protocol: Falsification-first · Preregistered

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.

A Four-Constant Alignment Matrix of Structural Response and Admissibility in Physical Systems

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UNNS Substrate Program · March 2026 · Structural Response Atlas

When Constants Change
but Structure Holds

A cross-constant investigation testing whether varying the fundamental constants of nature — α, μ, αₛ, αG — can break the structural ordering of physical systems. The answer is a precise, domain-specific no — and the exceptions reveal something deeper.
α · Fine-Structure μ · Mass Ratio αₛ · Strong Force αG · Gravity 0 Violations at Physical Values 7 Domains · 26+ Systems
Instrument: STRUC-I Chamber v1.0.4 Assessments: 166,000+ Constants tested: 4 Hard violations at physical values: 0

The Question

What if the fine-structure constant — the number that governs how electrons and photons interact — were slightly different from what it is? What if gravity were 20% stronger, or the ratio between the proton and electron masses shifted by a few percent?

The standard intuition is that everything would unravel. The chemistry would change. Nuclear binding would shift. Stars would form differently, or not at all. Physical structure seems fragile — precariously balanced at the specific values the constants happen to take.

This investigation tests that intuition directly. And the answer is more nuanced than either fragility or robustness — it is selectivity.

  1. Beyond Scale: How α Aligns Some Structures and Not Others
  2. Structural Persistence Across the Cosmos and the Earth
  3. The Geometry of Structural Laws
  4. The Geometry of Structural Admissibility in the UNNS Substrate

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