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 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."
Read more: The Cross-Domain Pulse: Structural Diagnostics in Gravity, Seismology, and Cosmology
A structural signature remains invariant under admissible operator perturbations whenever the structural separation margin exceeds twice the perturbation scale.
In this regime the operator parameter space decomposes into stability regions separated by discrete transition strata. Physical laws correspond to these stability regions in operator space.
These two papers establish a quantitative framework for determining when structural patterns qualify as laws. The first paper develops a perturbation-theoretic phase geometry of operator families and proves that structural invariance occurs precisely when separation margins exceed perturbation scale. The second paper clarifies how this phase geometry corresponds to the admissibility structure discovered in the UNNS substrate program — and connects the theory with the LI–LV structural arc and the Axis VI empirical chambers.
"Structural lawhood corresponds to interior position within admissibility geometry under bounded operator perturbations."
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."
Admissibility Geometry, Stratified Manifolds, and Observability through Invariance — a formal answer to the question: does the UNNS Substrate have a shape, and can that shape be observed?
The UNNS Substrate has long been described as the mathematical arena inside which structural laws emerge from recursive dynamics. But what does that arena look like? This paper gives a precise, measurable answer for the first time.
The shape of the substrate is not visible as a fault line or a physical surface. It is inferred through invariance geometry — the pattern of descent stability under admissible operator families. This work formalizes that shape as a stratified manifold inside the space of bounded linear operators, proves its convexity properties, and validates the predicted phase structure empirically using three earthquake events spanning two orders of magnitude in the Rigidity Modulus R.
The core result: structural lawhood in the UNNS Substrate exists precisely in the interior of admissibility margin 𝒜 > 1. The boundary is not a failure mode — it is a structural feature.
Read more: The Geometry of Structural Admissibility in the UNNS Substrate
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