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May 19, 20260 citationsOpen Access

A Numerological Coincidence for α and the RAR

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DSDavid B Smith

Key Points

  • To explore a numerological relationship between the fine-structure constant (α) and galaxy rotation through dimensional analysis.
  • Analyzed a 30-dimensional comparison space W = C⁵ ⊗ Λ² (R⁴).
  • Calculated α−¹cl and α−¹ including a leading term with N² = 900.
  • Presented outcomes as numerological observations rather than physical derivations.
  • Found α−¹cl ≈ 136.8585 and α−¹ ≈ 137.0359, aligning with empirical data within 0.3 ppm.
  • Identified a structured expression for the galaxy-rotation function g_obs = g_bar(1 − e − √g_bar/a_0.
  • Emphasized the findings as numerological observations without physical correlation.

Abstract

We present a compact numerological observation: a 30-dimensional comparison space W = C⁵ ⊗ Λ² (R⁴) yields α−¹cl = 208π²/15 ≈ 136. 8585. Adding the leading 1/N² term with N² = 900 gives α−¹ ≈ 137. 0359, within 0. 3 ppm of experiment. The same structure suggests the empirical galaxy-rotation function gₒbs = gbar (1 − e − √gbar/a₀). No physical derivation is claimed; the agreement is presented explicitly as numerology. Just pure numerology with no correlation to anything physical; a weird oddity on a planet with billions of opportunities for oddity every day.

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Cite This Study

David B Smith (2026) studied this question.

synapsesocial.com/papers/6a0bfe2d166b51b53d379693https://doi.org/10.5281/zenodo.20261875
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