DCT-AXS-01 · DCT cluster
Dimensional axis: geometric P₀ and the anti-dimension
Re-derives P₀ = cos(36°)/cos(18°) = 0.850651 from icosahedral midradius/circumradius geometry; derives P₀ from icosahedral geometry (P₀ first-principles); introduces the anti-dimension dual coupling β_up = 3/5.
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Abstract
The dimensional-axis closure paper re-derives P₀ from icosahedral midradius/circumradius geometry: P₀ = cos(36°)/cos(18°) = 0.850651 — a 0.041% match to the calibrated value 0.851. This derives P₀ from icosahedral geometry (P₀ first-principles) and re-tags 77 observables DERIVED_FROM_PRIMITIVES. The paper introduces the anti-dimension dual coupling β_up = 3/5 = V/F, the reciprocal of β = 5/3 = F/V. The pair {β, β_up} drives the β governs BEC condensation (downward), β_up governs anti-dimension dissolution (upward). Novel forward predictions: photon dispersion η = 1/12, n = 2 (CTA gamma-ray bursts 2028+); GW echo delay (3/5)·r_s/c·ln(r_s/l_P) (LIGO O5 2026–2028); BEC breathing-mode boson m* = ℏH₀/c² ≈ 1.44×10⁻³³ eV (PTAs 2030s); gravitational decoherence rate Γ = (3/5)·GM²/(ℏd) (table-top quantum gravity). 1/α improved to 0.003% via the 1/(E−χ) = 1/28 correction.
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