The Sixteen at Source

What AP30 carried. The proton formula of AP30 §6:

m_p/mₑ = 1836 + α·21·(1 − 1/(84π)) + α²·21·16/1836 + O(α³).

AP30 calls the second-order term “the leakage of the leakage — the break operating on its own maintenance,” and of its coefficient it says that the sixteen is carried in the verified formula but its structural decomposition from {21, 3, 4} is not established and is owed under KS-30.3; and that it is not Layer 3, which is 9. The first-order term is worth 0.152663699; the second, 0.0000097453.

What the measurement pins. Against CODATA 2022, the residual after the first-order term is 9.727 × 10⁻⁶ with the measurement’s uncertainty 3.2 × 10⁻⁸. Divided by α²·21/1836, the coefficient is 15.97 ± 0.05 — the corpus’s pre-registration of 2 August recorded the same pin, and that 336 = 21 × 16 is the only integer within 3σ that is a product of powers of {21, 3, 4}. It is not free. It must be 16 as a count; 15 is dead at 18σ and 17 at 20σ; any structure that gives 6, 8, 10, 12 or 20 is dead with them.

What arithmetic forces. From {21, 3, 4}, sixteen can only be 4 × 4. Neither 21 nor 3 combines to it. The decomposition is fixed before any reading; what is owed is what the two fours are.