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Structural persistence tests for mechanisms (not values)
A deterministic evaluation engine that classifies symbolic generators by whether they sustain recurrent structure under refinement.
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- Category: Labs
Operator XII (Collapse) as a Direct Test of Structural Fundamentality
This chamber empirically validates the canonical result that τ-closure is mechanism-defined: constants may be stable under recursion, yet remain non-primitive under refinement and collapse.
The absence of τ-primitives under unbiased grammar generation, combined with stable collapse-mode selectivity, provides direct empirical evidence that the UNNS substrate operates at a depth beyond simple numerical or syntactic structure.
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Primary τ-Invariants in the UNNS Substrate
Irreducible closure mechanisms · τ-closure · Classification, not discovery
1) What the Basis Theorem establishes
The paper Primary τ-Invariants in the UNNS Substrate (Closure, Relaxation, and Projection as Irreducible Structural Principles) proves a classification theorem about τ-closure. It does not enumerate constants, and it does not rely on numerical coincidence.
Instead, it establishes that exactly three irreducible closure mechanisms exist in the UNNS Substrate — mechanisms that remain invariant under arbitrary Φ-refinement and satisfy τ-closure.
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From class-level uniqueness to quantitative stability — with an empirical dashboard
This page presents the reference paper and the accompanying instrumentation dashboard. Together they formalize a strict UNNS claim: collapse is autonomous and acts as a pre-regularity principle—stability and universality appear prior to geometry, smoothness, or any PDE-based regularity story.
Why this matters (and why now)
Much of modern mathematics and physics begins after regularity has already been assumed: smooth spaces, well-behaved equations, stable limits. When irregularity appears, it is treated as an exception to be repaired. The UNNS Substrate asks a more primitive question: why does regularity appear at all?
