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Any system with a conserved quantity split between two channels defines a partition a + b = 1. From this partition alone, four dimensionless diagnostics are computed: resistance (a−b)²/2, stability bandwidth (√a+√b−1)/2, coupling 2√(ab), and active coupling √(ab)·(1−2√(ab)). Tested across five independent physical systems — 131 disk galaxies (SPARC), 650 interplanetary shocks, Planck CMB TT–EE spectra, binary black hole mergers (GWTC-3), and rocket propulsion mass fractions — the diagnostics consistently separate stable from unstable regimes, predict transfer efficiency, and identify saturation thresholds. The active coupling saturates at a universal ceiling of 1/8. The stability ratio converges to √2−1 across all systems within 1–2%. The Feuerbach gap between coupling architecture and stability boundary predicts scatter in galaxy dynamics beyond what mass alone explains (partial correlation p = 0.015). No free parameters, no dynamical models, no domain-specific assumptions. All results are algebraic consequences of a + b = 1 and the Euclidean altitude theorem.
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Title Four Diagnostics from a Conserved Partition: Stability, Efficiency, and Saturation Across Physical Systems
Any system with a conserved quantity split between two channels defines a partition a + b = 1. From this partition alone, four dimensionless diagnostics are computed: resistance (a−b)²/2, stability bandwidth (√a+√b−1)/2, coupling 2√(ab), and active coupling √(ab)·(1−2√(ab)). Tested across five independent physical systems — 131 disk galaxies (SPARC), 650 interplanetary shocks, Planck CMB TT–EE spectra, binary black hole mergers (GWTC-3), and rocket propulsion mass fractions — the diagnostics consistently separate stable from unstable regimes, predict transfer efficiency, and identify saturation thresholds. The active coupling saturates at a universal ceiling of 1/8. The stability ratio converges to √2−1 across all systems within 1–2%. The Feuerbach gap between coupling architecture and stability boundary predicts scatter in galaxy dynamics beyond what mass alone explains (partial correlation p = 0.015). No free parameters, no dynamical models, no domain-specific assumptions. All results are algebraic consequences of a + b = 1 and the Euclidean altitude theorem.
Work type Technical Documentation
Tags gravitational waves, binary partition, cmb, partition geometry, black holes, rocket propulsion, harmonic mean, sparc, geometric mean, stability diagnostic, thales theorem, galaxy dynamics, incircle, nine-point circle, feuerbach
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Identifier 2603154937048
Entry date Mar 15, 2026, 3:11 PM UTC
License Creative Commons Attribution 4.0
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Author. Holder Elias DeJesus. Date Mar 15, 2026.
Information available at https://www.safecreative.org/work/2603154937048-four-diagnostics-from-a-conserved-partition-stability-efficiency-and-saturation-across-physical-systems
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