The Placement

Proposition 5 — The Arena’s Commitment Lives in the Arena’s Coupling.

Statement. The commitment divides the persistence coupling α_G, and can appear nowhere else.

Argument. Under the arena reading the placement is forced, not selected. The commitment is the arena’s (§4). The corpus has already named the quantity that is the arena’s own cost of persisting — AP28 §2, locked: “G ↔ Axiom R (Record — persistence). The cost the arena pays to keep the break open.” The arena’s commitment can only appear in the arena’s coupling, and the arena’s coupling is G. There is no second candidate to eliminate: matter’s commitments are already booked as mass (§4, Corollary), so no mass is available to dress, and no other universal quantity is the arena’s persistence cost by the corpus’s own mapping. α_G∗ = α_G / (1 + ε); κ∗ = α_G∗ ℏc / 2. ∎

The elimination that a weaker reading would have needed is retained as corroboration, because it is independently sound: even if the commitment were sought on the mass side, that home fails twice — the arithmetic requires an unforced coefficient of one half to pass through m_e², and AP29 makes the booking a double count, since the held capacity is already the mass. The forced placement and the failed alternative agree, which is what completeness feels like when it arrives.

The placement fixes the paper’s footprint, and the footprint is the proposal’s discipline. Mass ratios: untouched, trivially (§4). The acceleration floor a₀ = C_S² · cH₀ / (2π), the Hubble prediction, and the dark-sector fractions: untouched at the formula level — none contains α_G. The nuclear binding ceiling of AP30 §8: untouched — it carries the puncture factor, not the compounded coupling. What moves: the predicted G, and the holding limit κ. And the audit this forces is wider than formulas: any corpus passage that consumes the predicted value of G or κ numerically — a worked example, a table, a Planck-scale estimate — moves with it, even where no α_G appears in the expression. D-CCC.3 books the full value-level audit, owed before adoption.