Project Context
This research constitutes the Scale Invariance Survey (Paper III) of the GM-MRH framework (the 11-dimensional Static Solid). It tests and documents the independent appearance of the GM-MRH structural constants across the solar system, spanning more than eight orders of magnitude in physical scale across nine independent measurement domains. It builds on the architectural theory of the companion paper (Paper I) and the observational prediction programme (Paper II):
Çakırlı, F. (2026a). The Gabriel-Möbius Moiré-Resonant Horn (GM-MRH): An 11-Dimensional Geometric Framework for Static Resonance and the Harmonic Metric Articulator. Zenodo. https://doi.org/10.5281/zenodo.20282881
Çakırlı, F. (2026b). 2026 Observational Tests of the GM-MRH Framework: Falsifiable Predictions and Verification Protocols. Zenodo. https://doi.org/10.5281/zenodo.20285078
Abstract
The Gabriel-Möbius Moiré-Resonant Horn (GM-MRH) framework derives structural constants from the geometry of an 11-dimensional non-orientable manifold (Çakırlı 2026a), including the Metric Impedance τ = 59, the Aperture Constant K114, the Metric Residual RD = 1/64 = 1.5625%, and the 144/19 = 7.578° inclination coordinate. If these constants are structural properties of the manifold rather than fitted parameters, they should appear independently across physical measurements that were not part of the original framework construction. This survey tests that prediction against solar system data using the forensic convergence standard of Paper I: independently measured physical properties, predating the framework, within RD of a framework constant or presenting genuine anomalies predicted by it.
The Belt Metric Anchor (3 Juno) presents three independent convergences on framework constants, alongside a newly identified illustrative correspondence — its orbital period approximates the square root of the lunar nodal precession cycle (4.314 years) to within 1.2% when both periods are expressed in years, offered as illustrative of the framework's Logarithmic Quadrature principle rather than as a precision convergence. The 144/19 = 7.578° coordinate, derived before any asteroid inclination was consulted, is occupied by 121 Hermione (7.567°, 0.14% — blind confirmation), 52 Europa (7.47°, 1.43%), and the Vesta family concentration at the belt's low-to-mid inclination transition boundary. Haumea's rotation period is recovered to 0.004% by 4.000 × (1 − RD × 19/14). Mercury's sidereal rotation period is predicted from τ = 59 alone to within 0.97%, and Venus's 13:8 → 8:5 Fibonacci gear expresses the 63/64 aperture limit, predicting 1.5996 years against the 8:5 synodic resonance of 1.600 years to within 0.02%. The 18.61-year nodal cycle produces a 1.3 ms periodic variation in Earth's length of day confirmed by over 50 years of IERS atomic clock data. The Saros eclipse cycle (6585.321 days) divides by τ = 59 to yield 111.616 — nearest integer 112, deviation 0.34% — formally grounded in Paper I via the Hidden Mode Coefficient (8 × 14 = 112), structurally twin to the RD derivation (8 × 8 = 64). The Crab Pulsar's discrete zebra stripe interference pattern is structurally consistent with the framework's Self-Interference Moiré architecture. Iapetus's unique unexplained equatorial ridge is consistent with the Metric Weld hypothesis at the Saturnian precessional boundary.
The entries span more than eight orders of magnitude in physical scale across nine independent measurement domains. No constant was adjusted to match any observation. Falsification criteria are provided for each convergence and qualitative entry. This survey establishes that the framework's constants were present in pre-existing solar system data before the 2026 prediction programme (Çakırlı 2026b) is adjudicated.
Publication Date: 2026-06-21