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What Crystals Reveal About
Realizable Structure
In Brief
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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A Candidate Structural Law
of Persistence
Admissibility Constraints Across Physical and Biological Systems — An Empirical Extension of the Universal Structural Law into the biological domain, establishing that the same instability bound governing atomic spectra, gravity, and large-scale structure also holds inside the fitness landscape of a self-replicating ribozyme.
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Nature Operates
at the Edge of Structural Failure
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Admissibility Geometry of
Atomic Spectral Ladders
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A CW-I test of structural persistence
in the cosmic web
Executive Summary
The CW-I (Cosmic Web Persistence Chamber I) applies a Gaussian coarse-graining ladder to three independent galaxy surveys and tracks the dominant eigenvector of the density-weighted inertia tensor as the smoothing radius grows. A survey-appropriate five-scale ladder R ∈ {5, 10, 20, 40, 80} Mpc is used for all three datasets, ensuring the coarse-graining operator acts on physically resolved density contrast rather than survey-volume geometry.
The primary finding is cross-survey convergence: all three independent galaxy surveys — DESI (N = 1,268,677), SDSS (N = 500,000), and 2MRS (N = 43,533) — receive verdict Structural Boundary on the survey-appropriate ladder. DESI achieves Sstruct = 0.9997 with total axis path L = 0.004°; SDSS achieves Sstruct = 0.841 with L = 1.07°; and 2MRS achieves Sstruct = 0.648 with L = 18.25°. No survey produces an intrinsic falsifier.
The three surveys span dramatically different cosmological depths, sky footprints, and galaxy counts, yet all three exhibit multiscale orientation coherence that persists across cluster and supercluster scales while remaining partially coupled to survey geometry. This convergence of independent observational datasets to the same persistence regime is strong evidence that the CW-I chamber is measuring a genuine multiscale structural property of the cosmic web rather than an artefact of any single survey.
"The cosmic web exhibits structural orientation stability that reproduces across three independent surveys spanning local, intermediate, and deep cosmological depth. This is a persistent geometric property of the galaxy distribution — not a statistical observation, not a coordinate artefact, not an isolated survey effect."
- The Cross-Domain Pulse: Structural Diagnostics in Gravity, Seismology, and Cosmology
- Cross‑Domain Admissibility Geometry: Budgeting Instability Across CMB Chains and Seismology Arcs
- Four Chambers, Three Earthquakes: Mapping Stability in the UNNS Substrate
- A Universal Curvature Sign Barrier in Admissible Recursive Systems