The Bode Filter: Logical Indexing and the Mass-Threshold Criterion

Title The Bode Filter: Logical Indexing and the Mass-Threshold Criterion Resource Type Preprint / Working Paper Creators Hallelujah, Paul Description Abstract The Solar Orbital Registry (SOR) hypothesis identifies a statistically significant correlation (P < 0.0002) between planetary orbital integers and polar atmospheric geometries (N=5, 6, 7). However, the Titius-Bode Law predicts a planetary body at 2.8 AU (the Asteroid Belt), which physically occupies the 5th nodal position. If the solar system were a purely passive physical system, this node should increment the planetary count, shifting Jupiter to Node 6 and Saturn to Node 7—decoupling them from their observed geometric resonances (N=5 and N=6). This paper proposes a "Logical Indexing" model to resolve this discrepancy. We posit that the Registry operates on a Mass Threshold Filter. The system is designed to ignore sub-planetary "noise" (debris fields) and assign indices only to significant bodies. This implies that the mechanism of polygonal formation is not a passive result of orbital distance, but an active, Tuned Resonance. Key Findings: The Mass Threshold Criterion: The Registry protocol defines a valid node only where mass exceeds a specific cutoff (M > M_{cutoff}). The natural accretion failure at 2.8 AU allows the system to "skip" the 5th physical node. The Tuned Receiver Hypothesis: The metallic hydrogen cores of the Gas Giants act as band-pass filters. Jupiter (I_{phys}=6) ignores the harmonic of its physical location and locks onto the harmonic of its logical assignment (I_{log}=5). The Octal Checksum: The observation of an Octagon (N=8) at Jupiter's North Pole serves as a "System Header," confirming a total count of 8 logical bodies, effectively validating the exclusion of the Asteroid Belt and Pluto from the registry. This paper suggests that the Solar System functions not merely as a gravity well, but as a calibrated logical directory, distinguishing between Matter (the Belt) and Worlds (the Index). Keywords Solar Orbital Registry, Titius-Bode Law, Magnetohydrodynamics, Technosignatures, SETI, Planetary Atmospheres, Jupiter, Saturn, Uranus, Geometric Cosmology, The Primer