A scale-free Higgs potential with discrete renormalization: kappa_lambda = 5/3 and m_H = 2v/sqrt(pi ln(1/alpha))

The LHC has established that the couplings of the 125 GeV boson follow the Standard-Model pattern at the 5–10% level, but the shape of the scalar potential — in particular the trilinear self-coupling — remains untested. We revisit the radiatively generated, scale-invariant potential V(φ) = Bφ4[ln(φ/v) − 1/4] (Coleman–Weinberg / Gildener–Weinberg form), whose shape fixes κλ = 5/3 and κ4 = 11/3 independently of normalization, and propose a new normalization principle to replace the loop sum that historically ruled this potential out (the top-quark loop makes the Standard-Model sum negative). Main results: If the effective theory's scales are generated multiplicatively in discrete steps of ratio α — so that the quartic running accrues in rungs of length ln(1/α) — and the per-rung increment is fixed by the two-channel braid structure of an elementary exchange (a unique Temperley–Lieb contact channel costing one closure loop, metered at the unit angular rate over the half-turn), then B = 1/[π ln(1/α)]. Consequently mH = 2v/√(π ln(1/α)) = 125.25 GeV, against the PDG world average 125.20 ± 0.11 GeV (+0.04%, 0.5σ) — equivalently the quartic coupling is the pure number λ = 2/[π ln(1/α)] = 0.12939 vs 0.12928 ± 0.00023. The internal alternatives are excluded by the data: the running coupling α(mZ) instead of the vacuum value (8.5σ), a Standard-Model loop contribution feeding the flow (51σ; even 10% contamination, 4.6σ), alternative angular measures (8–300σ). The look-elsewhere analysis is reported in full: a scan of 1134 simple closed forms yields three survivors, and the selection of 1/[π ln(1/α)] is structural (the 1/ln slot is forced by the discrete-rung hypothesis), not purely numerical. Falsifiable predictions: κλ = 5/3 (robust at the 0.3% level), with σ(HH) ≈ 0.55 σSM — on the destructive side of the triangle–box interference; testable at the HL-LHC, decisive at an FCC. κ4 = 11/3. Exactly SM-like tree couplings (κf = κV = 1) with vanishing invisible width. The sharpening of the mH world average tests the normalization linearly: a world average converging on 125.11 GeV would put the prediction at +1.3σ; below 125.0 GeV it fails. A French edition of the paper (higgs_selfcoupling_paper_FR) is included in the deposit. The analysis scripts (potential bench, normalization scan, angular-measure discriminant, Temperley–Lieb closure, discrete-flow tests) are included in the deposit and reproduce every number in the paper. The companion framework in which both hypotheses are motivated is documented separately (doi:10.5281/zenodo.21640710).