Odd Prime Source Audit

The actual audit results of Referee B trace the three branches of Case A/B/C from Document 17 back to named theorem sources one by one, rather than trusting previous self-derivations. $p=q$ additive: Banwait–Huang Proposition 2.9 Item 1 directly attributes this case to BSTW Theorem 9.21(c), whose proof lists five conditions ($p\ge5$, $p\nmid6N$, $p$ good ordinary for base $E$, $\bar\rho_{E,p}$ irreducible, existence of $\ell\parallel N$ such that $\ell\nmid D_K$ and residual ramified); checking 696.e1 item by item (support inertness implies ordinary, base mod-$q$ image maximal gives irreducible, taking $\ell=29$, $v_{29}(\Delta)=1$ hence $q\nmid1$, $29\nmid D_K=q$) all PASS, and citing Banwait Remark 2.10 confirms that semistability in this Item is only used to automatically generate a ramified witness; for non-semistable cases, treating the witness as a hypothesis is sufficient. Good ordinary $p$: directly applies the five conditions of Skinner Theorem C, taking witness $\ell=29$, PASS. Multiplicative $p=3$ and $p=29$: Skinner Theorem C explicitly states $p\ge3$, and the two mutually take each other as witnesses ($p=3$ takes $\ell=29$; $p=29$ takes $\ell=3$, since $v_3(\Delta)=1$), PASS. The document provides an important simplification that directly impacts the complexity of subsequent documents: because the mod-$\ell$ image of the base curve is maximal for all $\ell$, and a quadratic twist only tensors a scalar character, irreducibility is automatically preserved, so the ordinary branch absolutely does not need to be split into reducible/irreducible subcases anymore.