The Puncture — 1×ε

The axiom does not stop at 1:1. It says 1:1 + 1×ε. Perfect balance plus one unpaired element. The electron is a topological puncture — a hole connecting the unbroken vacuum to the cracked world (AP04 The Loop Hypothesis, AP05 The Break). It is not a fragment chipped off the mirror. It is a hole punched through it. The mass of the electron is the energy cost of keeping the hole open.

This puncture has a circular cross-section (Proposition 4). It is a tube connecting two topological regions, and the natural geometric measure of a circular boundary is π. The unpaired element — the one break with no partner — couples through this circular puncture. Its contribution to the gravitational coupling is weighted by the geometry of the hole: 1/π.

The total gravitational coupling is therefore α_G = α_em²¹ × (1 + 1/π). The first term is the 1:1 — the paired channels, the balanced structure. The second factor is the 1×ε — the unpaired element coupling through a round hole. The axiom wrote itself into the gravitational constant.

This determines the holding limit. The Lock, AP24, and AP14 write gravity as G = 2κ/m_e², with κ the holding limit. AP28 writes G = α_G × ℏc/m_e². These are one equation: matching them gives 2κ = α_em²¹ × (1 + 1/π) × ℏc, i.e. κ = α_G ℏc / 2. The holding limit is not a free primitive — the channel count fixes it. What remains the architecture’s one measured input is α_em itself; everything else, including κ and G, follows from it.