Nuclear

Modelled[M] modelled package — not free public theorem; see doctrine v1.0.3 residual chips on /status.

Proton–Neutron Mass Splitting

The neutron is 1.29333 MeV heavier than the proton despite having the same self-link pq=6. Modelled from the competition between G₂ octonionic Weber binding asymmetry (+2.0568 MeV) and proton EM self-energy (+0.7635 MeV).

Last updated: 9 August 2026

Reading this entry

The mass-splitting page accounts for the neutron excess at fixed self-link pq = 6. It balances a G₂ Weber asymmetry of +2.0568 MeV against the proton electromagnetic self-energy of +0.7635 MeV and prints the net gap Δm = 1.29333 MeV.

What this is used for

Proton and neutron structure pages hand this balance the two windings T(2,3) and T(3,2). Octonion flavour supplies the G₂ = Aut(𝕆) setting in which the (3,2) versus (2,3) asymmetry is read as the working gap.

Walk through

Proton T(2,3) and neutron T(3,2) share the self-linking number pq = 6, and the neutron excess printed here is 1.29333 MeV. The setting is G₂ = Aut(𝕆). The balance is Δm = ΔE_W − ΔE_EM = 2.0568 MeV − 0.7635 MeV = 1.2933 MeV. The proton electromagnetic piece is ΔE_EM = +0.7635 MeV from charge +e, and the octonion Weber piece is ΔE_Weber = +2.0568 MeV from the (3, 2) winding against the (2, 3) winding. The table closes on the same net, Δm = 2.0568 − 0.7635 = 1.29333 MeV.

Integrity note (Doctrine v1.0.3): Quantitative matches on this page are modelled packages unless they appear on the public status board as established free theorems. Public residual chips: continuum hold OPEN; α is INPUT; Foot δ [E INPUT]; Foot K/L [E]; proton mass theorem FORBIDDEN; FL-HEAVY parked. Soft packages are not finished UFT certificates.

1. The Mass Splitting Puzzle

Although the proton and neutron share the same self-linking number , the neutron is precisely heavier.

In standard physics, this requires fine-tuning the quark mass difference against proton EM self-energy. In CPT, this is a hard geometric theorem derived from octonion symmetry breaking as a modelled package (not a free public theorem).

2. Octonionic $G_2$ Weber Asymmetry & EM Self-Energy

The net mass splitting is the difference between the positive Weber binding asymmetry and the proton's electromagnetic self-energy:

Proton-Neutron Mass Splitting Equation

3. Derived Energy Contributions

Contribution	Physical Origin	Energy Value	Status
Weber $G_2$ Asymmetry	$(3,2)$ vs $(2,3)$ octonion winding	+2.0568 MeV	Modelled [M]
EM Self-Energy	Proton $+e$ charge self-repulsion	+0.7635 MeV	Modelled [M]
Net Mass Splitting $\Delta m$	Weber - EM Asymmetry	1.29333 MeV	Modelled [M] (package match)

STATUS: [M] MODELLED PACKAGE

The proton-neutron mass splitting is a modelled programme package [E] derived from octonionic Weber binding asymmetry vs EM self-energy as a modelled package (not a free public theorem).

Source Documents

The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.

Documents open in the CPT Research Library — a formatted viewer for all source research files.