AUTHOR'S CALL: [s14-m03] Recommendation: Keep parity on 14, Hodge endomorphisms on 15, Charles on 16, rational curves on 17, jump definitions on 18, and the reunited SO proof on 15 before Charles. No uniquely forced delivery choice. The candidate follows GPT 6 astra so each frame has one main idea.
GPT 6 astra: Use parity, Hodge endomorphisms, then a separate jump-definition frame.
GPT 5.6 sol: Use two frames; put eta, Pi_jump and gamma with parity; move sharpness to Charles.
Source: O:L616-635; I15:L523-527; V:L559-576.

NEEDS APPROVAL: [s14-m05] Recommendation: Keep the quoted candidate wording, formulas and arrangement on this slide.
Exact candidate text: "Why the reduction rank is even" | "$X_p/\Bbb{F}_q$ K3; $P_2(t)=\det(t-\operatorname{Frob}\mid H^2)$" | "$$q^{-22}P_2(qt)=h(t)\prod_i\Phi_{k_i}(t)^{\gamma_i}$$" | "$h\in\Bbb{Q}[t]$: no cyclotomic factor" | "$|z|=1$ $\Rightarrow$ $\operatorname{conj}(z)=z^{-1}$" | "Real roots: $+1,-1$, already in $\Phi_1,\Phi_2$" | "Roots of $h$: nonreal pairs; $\deg h$ even" | "Weil + Tate" | "$$\rho(X_p^{\mathrm{al}})=\sum_i\gamma_i\deg\Phi_{k_i}=22-\deg h\in2\Z$$"
Speaker notes proposed: "Tate identifies the full cyclotomic degree with the geometric rank. The conjugate-pair argument for $h$ uses Weil and rationality before using Tate."
SETTLED mathematical source: O:L616-635; V:L559-576; Deligne, Weil I, Thm. 1.6; finite-field Tate. Exact teaching arrangement still needs approval.

APPLIED, NEEDS APPROVAL (2026-09-14): [s14-m08] characteristic polynomial variable lowercased to t per the author, "let's use lower case t or x for our characteristic polynomials. in particular, avoiding u in slide 14".