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June 12, 20260 citationsOpen Access

GCFT CDN-166: The Velocity Window — Time-Domain Drag Decides the vᵣ-Linearity Question

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NHNicky Joseph Hubertus Catharina Hacquier

Key Points

  • This research investigates the behavior of drag force on moving gravitational sources within a new theoretical framework.
  • Time-domain integration of a linearized spintessence system using RK4 and spectral Laplacian techniques.
  • Implementation of absorbing sponge boundaries to analyze drag behavior across different velocities.
  • Analysis of the v_r-linearity within the velocity range, specifically focusing on low-velocity limits and wake dynamics.
  • Drag is linear for velocities approximately ≤ 0.1 with a constant force-to-velocity ratio within 7%.
  • Maximum drag occurs at around v* = 0.12, collapsing significantly by v = 0.6 with a local exponent of ~−7.
  • Proposes a conjecture on kinematic decoupling of fast systems and predicts observable anomalies in satellite data.

Abstract

CDN-166 settles theory debt D2 from the CDN-164 ledger. A time-domain integration of the CDN-163 linearized spintessence system (RK4, spectral Laplacian, absorbing sponge boundaries) yields a true drag force on a moving gravitational source — sign opposing motion, converged under domain size, run length, and timestep. The drag is linear in velocity only for v ≲ 0. 1 (F/v constant to 7%), peaks at v* ≈ 0. 12, and collapses by a factor ~500 by v = 0. 6 (local exponent ~−7): the fast source outruns the gapless quadratic branch that carries the wake. Verdict: the vᵣ-linearity assumed since CDN-139 is a low-velocity limit, not a law; the coupling must be read as acoh = −κc·f (ρ) ·W (vᵣ/v*) ·vᵣ/r² with a window function W. All κc-based results acquire a velocity-window caveat, and v* in physical units enters the ledger as new debt D5. Labeled conjecture: if v* falls between the MW–M31 approach (~110 km/s) and typical satellite velocities (~300 km/s), fast systems decouple kinematically — relieving the stream tension while preserving the CDN-139 flyby signal — and predicting a velocity-sorted anomaly pattern in the Gaia DR4 satellite sample, distinct from pure density screening. Channel split versus velocity matches CDN-163/165. Solver, results JSON, and figure included. By Nicky Hacquier (Aporion Dynamics) — Project Aporion; follows CDN-165 (DOI 10. 5281/zenodo. 20634700).

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Cite This Study

Nicky Joseph Hubertus Catharina Hacquier (2026) studied this question.

synapsesocial.com/papers/6a2ba5068101cf8926f03426https://doi.org/10.5281/zenodo.20634793
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