ONE CENTER · V3
One center, one axis: an exact alignment test for off-center observers
The alignment proof and local laws. No specific cosmological model required.
3 pages
RM POSTULATES · 19 SEPTEMBER 2026 CONSOLIDATION
The Universe is not infinite.And spacetime is abolished.
A finite spatial domain. One universal open time. Equations to put to the test.
These words express RM’s postulates and research direction, not an observational finding. RM postulates State Æ as a physical continuum and distinguishes universal time from the local cadence of physical processes. The results below retain their assumptions and domains of validity.
01A finite spatial domain
RM architecture and mechanical problemA finite spatial domain
and the mechanics of the Core
The cosmological model studied describes a finite physical domain containing a compact central body, the State-E Core, the surrounding bulk and a production boundary. This finiteness concerns the manifested spatial domain; it does not close universal time into a loop.
The Core’s density alone does not determine its exterior influence. Pressures, interface stresses and matching conditions participate in the sign and amplitude of the field. CART v5.1.0 sets out the radial compatibility conditions that these ingredients must satisfy together.
HÆ = H + g∂
The rate of the already manifested bulk, H, and production of new volume at the boundary, g∂, remain distinct contributions. Formation cost is not automatically the energy density left in the newborn volume.
02
Constitutive postulate · variational consequenceThe Global Elasticity Postulate
In the inhomogeneous branch of CART v5.1.0, elastic energy depends on the total volume of a specified physical reservoir. Its variation introduces that reservoir’s mean cadence into the local scalar constraint.
N = (1/V) ∫Ω N dVgD2N = QlocN + [3ε′z/(4P)] (N − N)
The mean term follows from the chosen global postulate and the declared action. The existence of a physical continuum alone does not select this energy from all possible functionals. The field must also satisfy the other equations and boundary conditions.
Source: CART v5.1.0, Sections III–VII, Eqs. (10), (14), (19) and (45).
Related but distinct result: homogeneous bulk closure
The Homogeneous Bulk Closure manuscript, revision v4.0.0, retains GHC–1 / GEC–1 / HBR–1. Under the declared matter–radiation balances, preservation of the conformal constraint gives:
H [3B′(e) + 3ρm + 8uγ] = s
B(e) = 2εz(e) + 3ε′z(e); s is the local matter-to-radiation conversion rate per unit volume. Closure depends on this source and the specified constitutive parameters. It imports no Friedmann equation or additional fitted dynamical response coefficient into this sector.
This is not a completed cosmology. Boundary production, perturbations and observational comparison remain separate tasks. Conicus3D is an external benchmark, not a model refuted by this calculation.
03
Geometric result under explicit assumptionsOne center, one axis: the standalone result
A complete physical configuration spherically symmetric about a center O, viewed from M with no velocity transverse to OM, preserves the SO(2) stabilizer of rotations around that axis. Any scalar sky map constructed covariantly under these rotations is therefore axisymmetric.
aℓm = 0 (m ≠ 0), dA × dB = 0
Nonzero dipoles arising from that same configuration are collinear, parallel or antiparallel. The result fixes neither their sign nor their amplitude. It does not prove that a cosmic center exists and is not a validation of RM.
04The test protocol
Local expansions · distinct channelsThe test protocol
and local depth laws
Symmetry fixes an axis; the physical channel determines the observable. Spatial depth s enters differently in an endpoint-potential difference, a propagation integral and a source count.
On mobile: scroll the table horizontally to read all four columns.
| Channel | Quantity | Order | Channel assumption |
|---|---|---|---|
| Observer kinematics | Doppler contribution to Z | s0 | Fixed observer velocity |
| Endpoint potential | Z− | s | Z = ln[N(M)/N(xem)] |
| Integrated scalar | OF− | s2 | Smooth scalar, local geodesic path |
| Absolute counts | (dN/dΩ)− | s4 | Smooth effective density ν |
| Relative count dipole | DN | s | ν(M) > 0 |
The distinction to retain: s4 describes the absolute odd part of counts. Their relative dipole is proportional to s at leading order when the local density is positive. This table does not compare four exponents of one common observable.
These laws concern small depths on a spatial slice, within the stated smoothness domain. A deep catalogue requires its own selection functions, mask treatment, source evolution and propagation laws. Local expansions alone are not a ready-to-use observational test.
01 · DEFINESpecify observables, selection functions and corrections before seeking an axis.
02 · ESTIMATEEstimate non-kinematic residual dipoles and their uncertainties, accounting for correlations.
03 · COMPARETest a common spherical origin: significant non-collinearity excludes it; aligned axes do not prove it.
Direct reading · versioned sources
Start with one question.
Open the calculation.
CART · V5.0
Can an Off-Center Cosmic Position Be Observed from Purely Spatial Geometry?
Global elasticity, the Core, pressures, matching and boundary production.
14 pages
BULK CLOSURE · V3
Constitutive Exclusion and Homogeneous Bulk Closure in Relativity of Matter
Homogeneous closure through GHC–1, GEC–1 and HBR–1, with its limits.
6 pages
Book V remains the general entry point
It receives ongoing updates; synchronization of Books I to IV is organized monthly. This editorial schedule does not change the scientific status of any result.
Detailed derivations and their assumptions are given in the manuscripts. The DOI links lead to the corresponding archival records.
Sources for this presentation
- One center, one axis: an exact alignment test for off-center observers
v3 · 19 September 2026 · 3 pages. - Can an Off-Center Cosmic Position Be Observed from Purely Spatial Geometry? · Zenodo / DOI
v5.0 · 18 September 2026 · 14 pages. - Constitutive Exclusion and Homogeneous Bulk Closure in Relativity of Matter · Zenodo / DOI
manuscript v3 · 19 September 2026 · 6 pages.