The Axiom and the Two Roles of ε

Written completely, the cycle that runs at AS is 1:1 + 1×ε @ AS [+1/137 | −1/137]. The break — the single +1×ε — is the persistent distinction potential: held, never cycling, what keeps S open; closing back would collapse the symmetric-with-distinction structure into undifferentiated Ø.

The flow — ±1/137 — is one operation read from two directions: writing outward as records are committed via the leakage, releasing back as records defragment via the replenishment, α-balanced at every AS instant. Both sentences are the Axiom chapter’s own, quoted at their locus, and this proof adds nothing to them; it reads them at event scale.

Two ε-roles therefore run through everything below and are never conflated. The splinter pays one grain standing, so that anything exists. Every event pays one grain passing, so that this thing exists rather than that one.

The author’s clause stands at its hedge and closes the loop between the scales: the permanent uncoupled remainder is the toll in a sense — what is needed for the break to persist. One coin, two scales.

Interpretive note, graded and worn openly (KS-ID.1 its open home). The corpus reads the held ε as the seat of the one interior. That reading is the author’s deepest conviction and is not proved physics; its formalisation debt (D-ID.1) stands reopened elsewhere in the registry, and nothing in this proof leans on it. It is stated because a proof about what every actualization costs should say, in one honest sentence, who the corpus thinks is paying.