Cpr = 4, version 5

Version 5 of Cpr = 4: A Closed-Form Relation Between the Proton's Mass and Charge Radius is on Zenodo: doi:10.5281/zenodo.23780522.

The relation itself is unchanged: r_p = 4ħ/(m_p c) = 0.841236 fm. What changed:

• Fairer comparison. Against CODATA 2022 (0.84075(64) fm) the measured index is Cpr = 3.9977 ± 0.0030, 0.76σ from four. Four reported radius values give 3.997–4.010 — but they are not four independent checks: CODATA relies partly on the same muonic-hydrogen data. The preprint now says so.
• Addresses as a hypothesis. In TOS the proton's charge radius corresponds to lattice rung 66 and its reduced Compton wavelength to rung 64, giving 4 = 2²; four is also the octahedron-to-tetrahedron volume ratio. These correspondences are now stated as hypotheses of the model, not as identities proven by the data.
• Priority dated 2013. We had dated Haramein's result to 2012. The journal records the article as received on 21 February 2013 and published on 27 April 2013, and we found no verifiable 2012 version, so we now date it 2013. Priority over Trinhammer–Bohr (2019) is unchanged.

Status: the relation is a dated, falsifiable claim; a future radius measurement can refute it.