Nuclear

Modelled[M] modelled package — not free public theorem; see doctrine v1.1.2 scope on /framework and /status.

Proton Structure

Programme language: T(2,3) is the hadronic sector candidate (structural). Absolute proton mass and continuum hold are not free public theorems (doctrine F: T(2,3)=proton theorem forbidden).

Last updated: 20 August 2026

Reading this entry

The proton page gives the structural seat T(2,3) on the Clifford torus, with winding numbers (p, q) = (2, 3). The recorded mass m_p = 938.272 MeV is printed beside that seat, and the Weber hold supplies the tube radius that keeps the confined photon on the knot.

What this is used for

Neutron structure, the mass-splitting balance, and the deuteron dance all start from this T(2,3) seat and its self-linking number pq = 6. The V4 engine reads the same winding pair (p, q) = (2, 3) when it builds the proton-side constants of the binding calculator.

Walk through

The proton is the torus knot T(2,3), with winding numbers (p, q) = (2, 3) and gcd(2, 3) = 1. The page lists the self-linking number pq = 6, the exchange phase (−1)^6 = +1, the charge +e with measured value +1.602×10^−19 C, the input mass m_p = 938.272 MeV, and the spin j = 1/2. The Weber hold is U_W(r) = (ke²/r)(1 − ṙ²/(2c²)). Stability sets dU_eff/dr = 0 at r = R_m, with angular momentum L = ℏ√(p²+q²) and effective potential U_eff(r) = (ke²/r)(1 − v_t²/(2c²)) + L²/(2m_γ r²), where v_t = c and L² = ℏ²(p²+q²). The stationary radius is R_m = (p²+q²)ℏ² / (ke² m_γ c² · (1 − 1/2)), and the frozen tube radius is R_m^(p) = (p²+q²)ℏ/(m_p c) = 13ℏ/(m_p c).

Integrity note (Doctrine v1.1.2): Proton = T(2,3) mass theorem remains FORBIDDEN. Structural lab reading: two internal lobes, not three QCD quarks. A probe of an intact proton has not demonstrated three quarks. Equivalence is to measured charge, moment, and form factors — not to uud ontology. See /framework and /status.

The Proton as T(2,3)

The proton has winding numbers on the Clifford torus. It is the torus knot — also known as the “trefoil knot” in knot theory. The winding numbers satisfy ✓ (required for a true knot, not a link).

The properties of the proton follow from these winding numbers:

Property	CPT Result	Measured	Status
Self-linking number		—	[E]
Exchange phase	(bosonic)	Bosonic (integer spin)	[E]
Charge	(winding = +1 net)	C	[E]
Mass	938.272 MeV/c² (T(2,3) package label — not free mass theorem)	938.272 MeV/c²	[M] (package match)
Spin	(from half-integer Hopf lift)		[M]

The Weber Hold

What keeps the T(2,3) proton stable? The confined photon is moving along a closed torus knot trajectory — it would escape the torus if not for a restoring force. The Weber potential provides this hold:

Weber potential — the velocity-dependent term provides a potential well at the Weber tube radius

The Weber Tube Radius

The Weber tube radius (the orbital radius of the confined photon in the proton) was established in the HD2 programme and frozen. For T(2,3):

Integrity Status

[M]

Modelled package. T(2,3) is a hadronic sector label under the multiplet writing rule — not a free public mass theorem (doctrine F). Reported numerical matches (e.g.

) and Weber-hold packaging are lab models pending promote review. See /status.

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.