The Vertices

The count is already proven; only the reading is new. AP28 Propositions 1–2 establish the coupling structure of the arena: six faces of ε, three spatial dimensions, one Actualization State. Faces couple to dimensions — eighteen edges. The Actualization State couples to dimensions — three edges. Faces do not couple to the Actualization State — Proposition 2, the page and the pen. Twenty-one edges. And the same proven structure has 6 + 3 + 1 = ten vertices.

The two costs of §1 are the two counts of this one graph. Leakage is transmission — an edge phenomenon: it flows along the couplings, per instant, C-bounded, twenty-one wide. Constitution is existence — a vertex phenomenon: the configuration is written into the elements themselves, once, R-recorded, ten deep. Under the arena reading the fit is exact: The Snap is what constituted the graph itself, and the commitment is written into the ten vertices at the instant they first exist. The corpus’s ten stands to its twenty-one as node to edge, as constitution to flow, as once to always. Nothing was added to obtain the ten. It was standing in AP28’s proof the whole time, waiting for the question that counts vertices instead of edges.

Honesty about status, in two halves. The count is DERIVED — it is the vertex set of a proven graph. The assignment — the commitment distributed one share per vertex, compounding to the quotient of §5 — is MOTIVATED, not forced, and it is booked as such (D-CCC.2), the exact mirror of KS-30.4’s uniqueness debt in AP30. And the assignment is empirically silent: the distributed and undistributed forms differ by about 24 parts per million in G, below anything the laboratories can currently see. Because §4 fixes the total at one ε regardless of any distribution, nothing numerical in this paper rests on the vertices. They are architecture — the right architecture, this paper holds — and architecture is claimed as architecture, not smuggled in as arithmetic.