An explicit initial Θ-datum with mixed reduction at a split prime

We exhibit an explicit initial Θ-datum in the sense of Mochizuki, IUT I, Definition 3.1: an elliptic curve in Legendre form over Q(√5) with ℓ = 7, for which the rational prime 211 splits in the field of moduli, so that one place of multiplicative and one place of good reduction lie above it. Every condition (a)–(f) of Definition 3.1 is verified individually, several by exact computation. The local invariants are e_g = 1, e_b = 105 and ord_211(q_b) = 29/7, the profile being tame at 211 since 105 ≤ 209. The configuration is not incidental. Because Definition 3.1(e) makes V a section of V(K) → V_mod, the tuples indexing a local tensor packet at a rational prime are constant unless that prime has several places in V_mod; and for the curve constructed here the only odd non-split places of multiplicative reduction are 3 and 5, carrying less than 1.24% of the relevant Tate contribution outside 2ℓ. Nor can the configuration be removed by a different choice of the bad set: the additional good-reduction hypothesis of IUT IV, Theorem 1.10 does not permit an actual bad place outside 2ℓ to be treated as chosen-good. Under one hypothesis (SA) about the source, isolated and discussed separately, the upper bound obtained in IUT IV, Theorem 1.10, proof, Step (v) by applying Proposition 1.2(iii) to a fixed target component is incompatible with the region it is applied to, with margin 8/7 at j = 1 and 88/7 at j = 2. We state (SA) separately, list the ways it can fail, and undertake to withdraw that application if the reading is shown to be wrong; we would regard such a demonstration as the more valuable outcome, since it would make explicit what the collection of possible images is at a tuple of mixed reduction type. What is not claimed. This is not a counterexample to the abc conjecture; it does not contradict the lower bound of IUT III, Corollary 3.12; and since the configuration cannot occur when the field of moduli is Q, results obtained over Q are outside its scope. Contents. The first report (11 pages) is the paper of record; a companion full draft (22 pages) gives the details. All arithmetic is exact and is reproduced by short scripts using only the Python standard library. A finite model checked by the Lean 4 kernel separates invariance of individual log-volumes from stability of a family of possible images. Large language models were used substantially in locating passages, cross-checking computations, drafting and adversarial review; the author is responsible for the claims, and the correction history is recorded in the paper.