An Axion Decay Constant from the G2 Constraint Sector: f_a = M_GUT × w_constraint (Work in Progress)

This is a preliminary report, circulated as work in progress. The Peccei-Quinn solution to the strong CP problem predicts an axion whose properties are governed by a single unknown scale, the decay constant f_a. We propose that within the G2 algebraic framework of prior work, this scale is set by the constraint sector: f_a = M_GUT × w_constraint = 4.28 × 10¹⁴ GeV, with M_GUT = 2 × 10¹ GeV the grand-unification ⁶ scale and w_constraint = 0.0214 the weight of the constraint sector (which governs CPT and conservation) from the symmetry-breaking analysis. The constraint sector is the natural home for a CP-conserving mechanism. Applying the standard QCD axion mass relation to this decay constant gives m_a ≈ 13–14 neV. We note explicitly that an earlier internal estimate of 29 neV was in error — traceable to an inconsistent choice of M_GUT — and the corrected value from the framework's own constants is approximately 13–14 neV. This lies within the search window of the CASPEr and ABRACADABRA/DMRadio experiments and below the ADMX range, making it falsifiable by experiments now operating. We present the decayconstant identification as the substantive proposal, the mass as its consequence, and the whole as provisional: the identification is physically motivated but not derived from first principles, and we set out the open problems plainly. Keywords: axion, strong CP problem, Peccei-Quinn mechanism, axion decay constant, dark matter, G2 algebra, CASPEr, work in progress