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.
Read more: Structural Regime Theory and the Universal Admissibility Framework
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.
Read more: Beyond Scale: How α Aligns Some Structures and Not Others
Crystallography can tell us what structure a crystal has — its symmetry, its lattice, its unit cell, its polymorphs. But there is another question hiding underneath all of that: when matter reorganizes itself into different ordered forms, how close does it come to the boundary where ordered structure stops being comfortably realizable?
We evaluated eight crystallographic material families — ferroic phase chains, polymorph oxide systems, a metallic pair, and a single-phase control — under the admissibility inequality. Every tested phase chain and polymorph family remained admissible. But they did not sit equally deep inside the safe interior. The law held throughout. And in doing so, it revealed a geometry.
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