Why Protons and Neutrons Stick Together: The Carry-Lock Mechanism
The Puzzle of Nuclear Binding
A nucleus is a tight cluster of protons and neutrons packed into a space about 100,000 times smaller than an atom. Protons are positively charged — they repel each other electromagnetically. Yet they stay bound. Something must overcome that repulsion.
That something is the nuclear force. It is: - Very strong at short range (it overwhelms electromagnetic repulsion) - Very short range (it essentially switches off beyond about 2 femtometres) - Selective: a proton-neutron pair binds more readily than proton-proton or neutron-neutron
The last point is particularly curious. Why should the proton-neutron combination be special? PLVS has a precise geometric answer.
Baryons as Phase Bubbles with Three Slots
In PLVS, the proton and neutron are both D=5 baryonic closures: phase bubbles whose interior contains one core node and three chirality slots. The slots can be of two types, T\(_+\) and T\(_-\), corresponding to the two tetrahedral chirality orientations of the C8 register.
The proton has the slot pattern \((2_+, 1_-)\): two T\(_+\) slots and one T\(_-\) slot.
The neutron has the pattern \((1_+, 2_-)\): one T\(_+\) and two T\(_-\).
The crucial fact: three is an odd number. No matter how you arrange three slots into T\(_+\) and T\(_-\) pairs, one slot is always left over. Every isolated baryon carries an unavoidable chirality residue. The proton’s leftover is T\(_+\); the neutron’s is T\(_-\).
The Lock-and-Key Mechanism
Now put a proton and a neutron together. Their slot patterns combine:
\[p + n = (2_+, 1_-) + (1_+, 2_-) = 3T_+ + 3T_-\]
Three T\(_+\) slots and three T\(_-\) slots — perfectly balanced. Every slot has a complementary partner. The two chirality residues cancel exactly. The system is stress-free.
Compare this to a proton-proton pair:
\[p + p = (2_+, 1_-) + (2_+, 1_-) = 4T_+ + 2T_-\]
Two T\(_+\) slots have no partners. The system carries residual same-handed chirality stress. It is not fully locked.
This is the PLVS nuclear selection rule: the \(pn\) pair achieves full complementary carry-locking; \(pp\) and \(nn\) pairs do not. The proton-neutron preference is not assumed — it follows from the odd slot count and the T\(_+\)/T\(_-\) chirality geometry.
The Three-Zone Force Profile
The nuclear force in PLVS has three distinct zones, all arising from the geometry of how two phase-bubble boundaries interact.
Zone 1 — Hard core (r < 0.38 fm): When two phase bubbles are forced very close together, their T\(_+\) and T\(_-\) boundary regions become coincident rather than adjacent. Instead of forming a constructive carry bridge, coincident complementary channels create destructive phase interference — carry conflict. The energy cost is \(S = 2K\) (maximum stress). This is the hard-core repulsion that prevents nucleons from collapsing into each other.
Zone 2 — Attraction (0.38 fm < r < 1.68 fm): When the bubbles are at the right separation — close enough to touch but not overlap — the T\(_+\) boundary of one Frasor is adjacent to the T\(_-\) boundary of the other at the complementary phase offset of \(\Delta\theta = \pi\). The carry stress drops to zero. This is the attractive nuclear lock. The energy is released, pulling the two nucleons together.
Zone 3 — No force (r > 1.68 fm): Beyond twice the bubble radius, the S² boundaries no longer overlap at all. There is no carry bridge, no force.
All three zones, and all three distance scales, emerge from a single input: the proton charge radius \(r_p = 0.841\) fm (which equals the bubble radius \(R_{\rm node}\)).
The Deuteron Binding Energy
The deuteron — a proton and neutron bound together — is the simplest nucleus. Its binding energy is 2.224 MeV (the energy you would need to supply to pull the proton and neutron apart).
PLVS computes this from the carry-lock geometry:
\[E_d^{\rm PLVS} = 3 \times m_p \times \frac{3}{17} \times \alpha \times \frac{2}{3} \times \left(1 - \frac{1}{4\pi}\right) \approx 2.224\text{ MeV}\]
The factors each have a specific PLVS meaning:
| Factor | Origin |
|---|---|
| \(3\) | Three T\(_+\)/T\(_-\) complementary lock events in the \(pn\) pair |
| \(m_p\) | Baryonic mass scale (empirical anchor) |
| \(3/17\) | Core carry coupling from the SCA channel structure |
| \(\alpha\) | Fine-structure constant (derived from register geometry) |
| \(2/3\) | SCA quorum: at least 2 of 3 carry channels must be active |
| \(1 - 1/(4\pi)\) | Hopf-Chern lobe capacity correction (the core depletes \(1/4\pi\) of the S² boundary) |
The result matches the measured deuteron binding energy to 0.014%. The only empirical input is \(m_p\); all other factors are derived from the PLVS geometry.
What This Means
The nuclear force in PLVS is not a separate force added on top of the framework. It is a direct consequence of the phase-bubble boundary geometry — the same geometry that gives the proton its charge, its mass, and its size. When two phase bubbles come into contact, the nature of their boundary interaction depends entirely on their internal T\(_+\)/T\(_-\) slot patterns. For the \(pn\) pair, the geometry says: lock. For \(pp\) and \(nn\): stress.
The nuclear binding force is the read-out of the carry-lock mechanism at the two-bubble scale.
Full derivation including the nuclear force profile and Hopf-Chern lemma:
Technical Supplement v4.4 — doi:10.5281/zenodo.20472246