CODATA 2026 Preregistration

Three competing predictions for 1/α, recorded before CODATA 2026 publishes.
The git commit timestamp is the proof of priority.

The Framework

The integer part of 1/α is derived from E₇ Lie algebra topology:

The fractional part comes from a self-consistent equation encoding one-loop vacuum polarization on the E₇ ALE space:

Three closed-form candidates for r are registered below. Each is stated with its derivation, or honest lack thereof.

Candidate 1 DERIVATION

Derivation chain

The McKay correspondence maps finite subgroups of SU(2) to ADE Dynkin diagrams. The binary octahedral group 2O (order 48) — the symmetry group of the star tetrahedron inscribed in C³ — maps to the affine E₇ Dynkin diagram.

Attach a semi-infinite chain at the branch node (node 2, degree 3) of the E₇ Dynkin diagram. This models the E₇ discrete structure coupling to flat-space continuum. The scattering phase shift at the golden angle k = 2π/5 (energy E = 1/φ) gives δ = 0.798, capturing graph topology but missing Lie algebra structure.

The Lie algebra correction:

The ratio 19/18 counts total degrees of freedom (133) versus internal oscillations (126 roots). The 7 extra dimensions are the Cartan subalgebra — the part that couples to the continuum. The roots stay internal; the rank radiates out.

Physical picture: E₇ is a drumhead (133-dimensional discrete structure). Flat space is the air. r measures how efficiently the structure radiates into the continuum. The arctan wrapping arises from impedance matching at the boundary between discrete and continuous spectra.

Candidate 2 DERIVATION KILLED

Original derivation (killed)

√(2/π) is E[|X|] for X ~ N(0,1) — the mean absolute value of a standard Gaussian. The original proposal was that r encodes the Gaussian field average of the U(1) gauge orbit, derived from the Eguchi-Hanson spectral determinant on the A₁ ALE space (resolved C²/Z₂).

Why it was killed

The spectral determinant test: does Δζ'(0) on the A₁ ALE space equal log(π)?

If yes, √(2/π) emerges naturally as a spectral coefficient. The computation (double Hurwitz zeta function, verified to 12+ digits):

The number that DOES appear naturally is log(2) (from the double sine function on S³/Z₂), consistent with det(Cartan of A₁) = 2. The Eguchi-Hanson metric does not produce log(π). The derivation is dead.

Candidate 3 NO DERIVATION

Derivation

There is none.

4/5 is the continued-fraction convergent [0; 1, 3, 1] of r_exact. The next CF coefficient is 35 (large), making 4/5 the best simple-fraction approximation. One can note 4/5 = max(Kac) / (max(Kac) + min(Kac)) = 4/(4+1), but this is post-hoc pattern matching with no physical mechanism.

CODATA 2026: The Decisive Measurement

CODATA 2026 is expected to achieve ~0.05 ppb uncertainty in 1/α, a 3× improvement over CODATA 2022. This comes from improved electron g−2 measurements and 5th-order QED calculations.

Mutual distinguishability at 0.05 ppb

All three candidates are mutually distinguishable at >3σ. CODATA 2026 resolves the question completely.

Survival analysis

If the CODATA 2022 central value holds:

Kill thresholds

How much improvement over CODATA 2022 is needed for a 3σ kill (assuming the central value does not shift)?

C2 and C3 are killable with the expected 3× improvement. C1 requires 352× improvement — far beyond any foreseeable measurement.

What Each Outcome Means

Honesty

Independent Verification

All values computed with mpmath at 60-digit precision. Verify with:

import mpmath
mpmath.mp.dps = 60

r1 = mpmath.atan(mpmath.sqrt(mpmath.mpf(19)/18))
r2 = mpmath.sqrt(mpmath.mpf(2)/mpmath.pi)
r3 = mpmath.mpf(4)/5

for name, r in [("arctan", r1), ("sqrt(2/pi)", r2), ("4/5", r3)]:
    B = mpmath.mpf(274) * 137 + mpmath.pi**2
    disc = B**2 - 4 * 274 * r
    x = (B + mpmath.sqrt(disc)) / 548
    print(f"{name}: 1/alpha = {mpmath.nstr(x, 18)}")