The Denomination and the Two Faces

The denomination is α, by two arguments on two jurisdictions that could not have disagreed without breaking the axiom’s own semantics.

First: the flow is one operation, so its two directions carry one currency — and the writing direction’s currency is α by construction, the per-channel coupling AP28 built.

Second: the grip that opens is electromagnetic, so breaking it is priced in the grip’s own coupling — while thermodynamics decides when a break is affordable, never what it is worth: the modulator, not the mint.

And the rivals were weighed, each against the event it must price: mass books and persists, and the toll is spent; c bounds propagation and prices no crossing; G holds all channels and never lets go, so it has nothing to charge for letting go; stiffness and direction are readings, not currencies. α is not chosen. It is what remains.

The two faces, ruled. The toll is one singular cost calculated at two dimensions.

The energy face is the outside: ordinary, unchanged, carrying nothing but the standard threshold energetics every break already involves — which is why no budget anywhere owes it a line, and why the ceilings of §10 never had jurisdiction: not because the toll is small, but because it was never in their dimension.

The possibility face is the inside, where the toll actually lives: dimensionless, one ε-grain of α-worth — the alternatives not taken.

And the reading closes on canon’s own equation: awareness is the coupling capacity the break creates, and energy is that capacity expressed at the now — E ≡ κ(B)AS — so the two faces of the toll are the two faces of the corpus’s own definition of energy, met at a single event.