Higgs Boson Mass (n = 5 route)

τ-Formula

m_H = (4 − ι_τ³/(1 − 5κ_ω)) / κ_ω → 125.26 GeV

Derivation

An earlier derivation (Wave 3, Registry IV.T151) used $n = 5 = W_3(4)$, the third Waring number at four terms. The formula

m_H^(n=5) = 4 - ι_τ^3 / (1 - 5κ_ω)κ_ω · (scale factor),

where $κ_ω = ι_τ / (1 + ι_τ)$, gave $m_H ≈ 125.26$ GeV at $+493$ ppm. The $n = 7$ result supersedes this, improving precision by a factor of 60 and providing a cleaner structural derivation (the integer 7 arises from the lemniscate geometry itself, not from a Waring function).

The shift from $n = 5$ to $n = 7$ illustrates the research programme’s self-correction. Wave 3 identified the correct structural form (a rational function of $ι_τ$ and sector couplings) but assigned $n = W_3(4) = 5$. Wave 5 recognized that $n = 7$ has a more direct structural derivation from the lemniscate geometry, and the precision improved from $+493$ to $+8$ ppm. Both derivations are honest readings of the $τ$ structure; the second is the sharper one. The hierarchy problem is simultaneously dissolved: there is no UV cutoff in $τ$, hence no quadratic divergence $δ m_H^2 ∼ Λ^2$ and no fine-tuning problem.

Source

This prediction is derived in the Numerical Physics Ledger (Chapter 60 — mass-spectrum), Books IV–V of Panta Rhei.