The Dial and the Axis: An Irreducible-Bias Perspective on Dynamic Alignment in Allocation Settings

Review state: four-party review complete — Kimi red-pen round, GPT foundation review, 智谱 (Zhipu GLM) boundary patrol, and Qwen formalization review all incorporated (v0.4). 13 tickets across the five candidates (12 accepted, 1 merged-closed: P1-C-Q03 into P1-C-Q01). Lower bound by Neyman-Pearson optimality (simple alternative), constant c = z_{1-alpha} + z_{1-beta}. Candidate propositions are labeled as such. Spinout track outside the Roman-numeral main sequence; Map registration ships with v33 (XL v1.3 batch). Changelog v4 (2026-08-23): round 4 (Qwen formalization review) applied — 13 tickets: P2-A-Q01~03, P2-B-Q01~03, P2-C-Q01~02, P1-C-Q01, P1-C-Q02, P1-C-Q03 (merged-closed into Q01), P1-C-Q04, P2-C-Q03. This paper: P2-A-Q01~03 (single-step labeling; direction-coverage/chord-subdivision formalization; Def 1 declares d(x,y)=norm(x-y)). Version stamp aligned (draft v0.4 / record v4).