constants: document α guard-digit and uncertainty rationale#1708
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α is stored as 0.00729735256434, one digit past the CODATA-2022 recommended 7.2973525643e-3. The last digit (...34) departs from the bare 1/137.035999177 continuation (...33) on purpose: it makes the α-dependent constants (μ₀, ε₀, me, a0, re, σe) round to their CODATA-2022 recommended values, which are each rounded independently and so are not mutually consistent at the 1e-12 level. The σ field (1.14e-12 = α·u_r) likewise reproduces NIST's u(α) = 1.1e-12 and the dependent CODATA uncertainties (re 4.7e-10 = 3·u_r(α), σe 9.3e-10 = 6·u_r(α)). The deviation is far below α's own uncertainty. Comment only; no value change.
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α is stored as 0.00729735256434, one digit past the CODATA-2022 recommended
7.2973525643e-3. The last digit (...34) departs from the bare 1/137.035999177
continuation (...33) on purpose: it makes the α-dependent constants
(μ₀, ε₀, me, a0, re, σe) round to their CODATA-2022 recommended values, which
are each rounded independently and so are not mutually consistent at the
1e-12 level. The σ field (1.14e-12 = α·u_r) likewise reproduces NIST's
u(α) = 1.1e-12 and the dependent CODATA uncertainties (re 4.7e-10 = 3·u_r(α),
σe 9.3e-10 = 6·u_r(α)). The deviation is far below α's own uncertainty.
Comment only; no value change.