The Bag and the Cavity — where mainstream confinement already puts the proton

The direction lists asked for the bag-model correspondence, and it is computed here exactly, with the credit stated first: the MIT bag model (Chodos et al., 1974) is standard physics. Three massless quarks in a spherical cavity, each costing the lowest Dirac-cavity eigenvalue (the Dirac analogue of the Bessel zeros this deposit's peak-count papers are built on), held shut by a vacuum pressure B. Minimising the bag energy at the nucleon mass gives, with zero tuned numbers: cavity radius 1.72 fm, MeV. The standard corrected fit (zero-point and gluon terms, credited, not rerun) moves that to 1.0–1.2 fm — the ledger's own . So the narrow point this deposit is entitled to: the "quantum cavity of nucleon size" this framework reasons in is not its invention — it is the size mainstream confinement physics assigns when it plays the same game, with the crudest version landing within a factor of two of the right scale untouched, and the corrected version landing on . One scale, every road: the measured proton (0.84 fm), the ledger's Coulomb (1.20 fm), the bag (1.0–1.7 fm), the radius scoreboard's 1.238 fm (Paper 86). No new constant appears anywhere. And one deflation, added the same day after an external check: this convergence is expected, not surprising — ~1 fm is simply the QCD confinement scale that all of these quantities inherit, so "one scale, every road" is a statement of consistency with known physics, never evidence of independent agreement between methods. It earns vocabulary, nothing else. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.