Neutral winding proto-clock claim boundary

This theorem asserts the entire proposition just described: with $P_c(x)$, $Q_c(x)$, $\theta_r$, $\prec_r$, $O_a$, $D_k$, $R$, and $B(\alpha)$ having the expanded meanings above, it simultaneously asserts (i) the principal interval bounds, reconstruction identity, cut-independent reconstruction and phase, and the equation $Q_{-\pi}(r(e))=-(-Q_{-\pi}(r(e)))$; (ii) irreflexivity and transitivity of the order induced by every reading, comparability under injectivity, exact agreement with an existing linear order under strict monotonicity, and existence of the specified non-strictly-monotone reading $0,4\pi,2\pi$ on $\operatorname{Fin}3$; (iii) the identity, composition, increment preservation, order preservation, unique-offset result on nonempty event types, corresponding integer deck-shift laws, phase invariance, order invariance, and faithfulness $D_k(r)=r\iff k=0$ on nonempty event types; (iv) phase inversion, order reversal, and negation of deck shifts under pointwise sign reversal; (v) both universally quantified constant-$\operatorname{Unit}$ quotient assertions for integer multiples of $2\pi$; and (vi) $B(\alpha)\iff\alpha<1$ together with $\neg B(1+h)$ for every $h\ge0$. Every event type is allowed to be empty except where a Nonempty assumption is explicitly present, so the corresponding eventwise clauses can be vacuous on an empty type.