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"We report the first dynamical extension of the Thales partition framework from static geometric diagnostics to predictive integration. A Thales Lagrangian — whose kinetic term is the Poincaré metric induced by the semicircle embedding G(χ) = 1/(4(1−χ²)) and whose effective potential is calibrated from 27 galaxies — is integrated outward from the central baryon fraction to predict rotational velocities for 107 held-out disk galaxies from the SPARC database. 85.0% of predictions fall within the incircle of the observed partition, matching the 83.7% natural incircle occupancy of the sample. The Feuerbach gap correlates with absolute prediction error at rs = +0.415 (p = 8.7 × 10⁻⁶), establishing it as a forecastability parameter. Mass-stratified accuracy ranges from 0.6% RMS for massive spirals to 12% for dwarfs, spanning two orders of magnitude as predicted by the diminishing-returns property of the incircle–mean identity r_in = h/(1 + √(1+2h)). Low-mass failures are interpreted as steep-regime amplification, not hidden. The geometric stability architecture of the Thales partition controls both system robustness and model accuracy. No modification of established dynamics is proposed
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Title The Thales Lagrangian as a Regime-Aware Predictive Instrument: Incircle Hit Rate, Feuerbach Gap Sensitivity, and Mass-Stratified Performance Across 107 Disk Galaxies
Excerpt/Description:
"We report the first dynamical extension of the Thales partition framework from static geometric diagnostics to predictive integration. A Thales Lagrangian — whose kinetic term is the Poincaré metric induced by the semicircle embedding G(χ) = 1/(4(1−χ²)) and whose effective potential is calibrated from 27 galaxies — is integrated outward from the central baryon fraction to predict rotational velocities for 107 held-out disk galaxies from the SPARC database. 85.0% of predictions fall within the incircle of the observed partition, matching the 83.7% natural incircle occupancy of the sample. The Feuerbach gap correlates with absolute prediction error at rs = +0.415 (p = 8.7 × 10⁻⁶), establishing it as a forecastability parameter. Mass-stratified accuracy ranges from 0.6% RMS for massive spirals to 12% for dwarfs, spanning two orders of magnitude as predicted by the diminishing-returns property of the incircle–mean identity r_in = h/(1 + √(1+2h)). Low-mass failures are interpreted as steep-regime amplification, not hidden. The geometric stability architecture of the Thales partition controls both system robustness and model accuracy. No modification of established dynamics is proposed
Work type Technical Documentation
Tags geometric mean, stability bandwidth, thales lagrangian, euler-lagrange, partition geometry, poincaré metric, ads, predictive integration, galaxy rotation curves, feuerbach gap, regime classification, sparc, baryon fraction, forecastability, dark matter, hyperbolic geometry, harmonic mean, diminishing returns, incircle
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Identifier 2603154942684
Entry date Mar 15, 2026, 10:08 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/2603154942684-the-thales-lagrangian-as-a-regime-aware-predictive-instrument-incircle-hit-rate-feuerbach-gap-sensitivity-and-mass-stratified-performance-across-107-disk-galaxies
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Registration: 2603154942684
