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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."
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Structural Phase Diagnostics
Across Physical Domains:
Gravity Joins Seismology and Cosmology
Executive Summary
The UNNS cross-domain program tests whether structural admissibility signatures — patterns predicted by the substrate framework — appear consistently across physically unrelated systems. Two domains had already been examined: the cosmic microwave background (CMB multipole structure) and global earthquake distributions (seismic arc geometry). Both produced clear structural contrasts between real and synthetic systems.
This report introduces the third domain: planetary gravity fields. Chamber GRAV-I applies a spectral axis dominance diagnostic to spherical harmonic decompositions of Earth, Moon, and Mars gravity models, sweeping the harmonic degree from L = 2 to L = 300+. All three planetary bodies exhibit persistent distributed anisotropy — directional structure that survives spectral extension — while synthetic random fields behave qualitatively differently.
"The same structural diagnostic framework — built from admissibility geometry — produces meaningful, consistent output across seismology, cosmology, and planetary gravity. This is not a coincidence. It is the fingerprint of a substrate-level structural law."
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Instability is Structurally Budgeted
A Cross-Domain Empirical Certification in Seismology and Cosmology
Executive Summary
A fundamental question underlies much of modern physics: why is the universe structured? Why do cosmological features persist, why do seismic displacement fields cohere, why does large-scale order survive the relentless pressure of perturbation and noise?
The UNNS Axis VI programme answers this question with a structural law, not a model parameter. Working directly with real cosmological data from Planck CMB observations and three independent earthquake displacement datasets, a suite of purpose-built experimental chambers tested whether spectral features under resolution variation obey a universal admissibility constraint.
They do. The central finding — that the inversion count is always bounded by the matching number of the vulnerable gap set — was never violated across any dataset or domain. And cosmology, it turns out, lives right at the edge of that boundary.
"Physical systems do not explore configuration space freely. They move along admissible operator paths. Instability is constrained — and the constraint is structural, not domain-specific."
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Abstract
We present the UNNS Substrate's first quantitative admissibility phase framework, emerging from a four-chamber seismic analysis suite (LXV) applied across three independent rupture systems. Prior to this work, the Rigid–Nonrigid Principle (RNP) was a structural separation criterion — a conceptual distinction between structures that descend and those that are representational artifacts. It is now a measurable phase theorem with computable descent conditions, boundary degeneracy bounds, and matching-theoretic inversion budgets.
The central empirical discovery: displacement fields admit a single global orientation unless invariance stability forces minimal decomposition. Kumamoto (k=2), Ridgecrest (k=1), and El Mayor (k=1) present both cases in clean contrast. Magnitude does not trigger splitting. Directional incompatibility under admissible operator nesting does. This is not rhetoric. It is a falsifiable, cross-validated pattern — and it is exactly what a substrate-level structural law looks like.
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A Theorem Proved by Elimination
Executive Summary
The UNNS recursive substrate has now crossed a defining threshold. Four consecutive chambers — each designed to probe a distinct mechanistic escape route from positive curvature — have all returned the same answer: CERT_NEG = 0. Not a single certified negative curvature cell exists anywhere in the 231-cell operator simplex, across any tested axis of intervention.
This is not a failure to find something interesting. It is the finding. The unanimous null, sealed by a 2³ full factorial intervention design and confirmed across 7,400+ independent cell-regime records, constitutes the empirical foundation of a new structural theorem:
"Admissible recursion preserves positive curvature — by algebraic necessity, not by accident."
This article presents the chambers, the structural constants they revealed, the conjectured theorem, and why — in the landscape of mathematical analysis — this result is likely unprecedented in its exact form.