Two-valuedness against measurement

In 1925 Pauli called the electron's extra quantum number "a peculiar, classically non-describable two-valuedness". I set nine theories that give that two-valuedness a mechanical picture beside the published measurements that bear on them. A neutron's wave returns after 716.8 ± 3.8° of precession, not the 360° of any rotating body. Bell tests give S = 2.697 ± 0.015 against the limit of 2 for answers preset at the source. Gravity shows no fourth direction above 38.6 µm, and no Kaluza–Klein graviton appears below 2.3–4.6 TeV in the models searched. Two theories are contradicted (the rotating charged electron and the preset local axis), six are not contradicted because no measurement contradicts a number they fix, and one states no number to test. Beside the paper I scored nine relations of gravity and quantum physics against 17 published measurements, and 29 predictions written and hashed before their measured values were loaded, across 17 fields: 16 agree, 12 contradicted, 1 agree on a secondary source only, and 1 with no measured value yet.

716.8 ± 3.8°neutron return angle; 94 standard errors from 360°
S = 2.697 ± 0.015Aspect 1982; 46.5 standard errors above the preset-answer limit 2
S = 2.42 ± 0.20loophole-free, electrons 1.3 km apart (Hensen 2015)
< 38.6 µmlargest Yukawa range of gravitational strength allowed (Lee 2020, 95 %)
2 contradicted · 6 not contradicted · 1 states no numbernine spin-based theories, Table 2 of the paper
16 agree · 12 contradictedblind predictions, 29 scored, hash fixed before scoring

PaperThe full text, HTML and PDF, 38 references with DOIs. ExplanationThe paper section by section, in plain words. IntuitionOne wave tied at two ends; no fourth direction. Drawn. ExperimentsEvery test: question, measurement, residuals, agrees or contradicted. Proof18 claims, each with its measurement, number, uncertainty, DOI and script line. Raw dataEvery dataset as CSV and JSON, with hashes, timestamps and a README. ExamplesThe rope simulation, the CHSH run, the 720° return, worked numbers. ReproduceOne command recomputes every number; expected output and its hash.

Status: final draft of 2026-11-07, not peer reviewed. Corrections with a source are welcome at author@ratnamchandra.com.