配对结构:确认动作与约束读出的公理化构造 / The Pairing Structure: An Axiomatic Construction of Confirming Actions and Constraint Readouts
Qin Qin
Axiomatic construction of the binding between a confirming action and a constraint readout (Chinese with English full text). Axiom form: the Pairing structure (idempotent confirming action f x discrete constraint readout r) — the pure-mapping layer with minimal assumptions (no linearity, no inner product, no completeness, no topology). Core theorems: the pairing core of 7 (readout stability; collapse-point compatibility; motion-swallowing non-injectivity — irreversibility of collapse proved at the pure-mapping layer; the confirming subspace as the range; the two faces of commutation with an explicit non-commuting counterexample; a non-degenerate instance) and 12 deep pairing theorems (complete classification of idempotent dynamics; readout-collapse exclusivity; window-intersection geometry). Load-bearing mappings: three-layer pyramid — pure-mapping layer (19 items) x inner-product layer (projection postulate, eight blocks, 53 items, incl. continuous-spectrum ProjVM with no-atom finite collapse) x spectral layer (EBK quantization, 10 items; the pi/hbar division of labor made theorem-grade). Specialization: the quantum measurement postulate as the quantum-domain special case (third member of the specialization family). Meta-constraint corollary: c/alpha/Lambda rows at theorem grade (45 items; PureAnchor band, zero hits in 1,323 monomial combinations). All core content Lean 4 formalized: 195 items, zero sorry, 20 files (#print axioms within the standard three). Honest boundaries: no in-system origin for Born weights (largest open problem); sigma-additivity awaiting upstream; bpi left blank. Companion to the popular-science essay 'Where does energy live'. v1.1 (2026-09-28): replication repository linked: https://github.com/vortex-QC/pairing-structure (Lean 4 zero-sorry minimal root). No content changes.
•Sep 28, 2026•2 citations