Connections

AP06 (The Leakage Constant)

α_em as the leakage constant provides both the dynamic maintenance rate and the perturbative expansion parameter. The proton’s mass is fundamentally set by the substrate’s leakage rate operating across the channel geometry.

AP10 (The Dimension)

The numbers 21, 3, and 4 all originate in AP10. Three spatial dimensions → three faces → 21 channels. Four spacetime dimensions. The entire formula is downstream of AP10’s geometry.

AP19 (The Direction)

SU(3) from three faces. The face projection (Layer 2) and the exchange matrix (Layer 3) both arise from AP19’s derivation of the strong interaction from the manifold’s three-face structure.

AP20 (The Proof)

Axiom independence. The additivity of resistance layers (Lemma 1) depends on the independence of {S, B, R, C} proven in AP20.

AP28 (The Constant)

The 21-channel count. The G derivation. The connection between α_em and the gravitational constant. AP30 and AP28 share the same structural integers because they describe the same manifold from different angles.

AP29 (The Actualization Proof)

Coupling capacity κ(B). AP29 establishes that mass is κ(B) × AS — coupling capacity actualised. AP30 gives the specific resistance count for the proton: κ(B) for the 3-face, 21-channel bound state equals 1836 + O(α_em).

The Fusion Programme

The binding energy ceiling BE/A ≈ α_em × (1+1/π) × m_N (Clarification 6) no longer contains an empirical mass. With m_N/m_e derived, the ceiling is fully expressed in terms of {S, B, R, C}:

BE/A_ceiling = α_em × (1+1/π) × [1836 + α_em × 21 × (1 − 1/(84π))] × m_e

No free parameters remain in the nuclear binding energy ceiling.

The three fundamental quantities

AP03 establishes three fundamental quantities: c (propagation), ℏ (record), G (persistence). AP28 derives G from α_em, m_e, ℏ, and c. AP30 derives m_p from α_em, m_e, and manifold geometry.

Together with AP03, the axioms now express all fundamental scales in terms of the axioms.