Certified Murmurations over Function Fields: Unconditional Rank Labels and Two-Witness Certificates

First two-witness certified murmuration study over function fields. We work in the CM family y² = x³ + x + D(t) over 𝔽_q(t), q ∈ {7,11,13}, deg D ≤ 5 — the regime where Birch–Swinnerton-Dyer is a theorem (Kato–Trihan, Invent. Math. 153, 2003), so every in-family rank label is unconditional. We deliver: (1) a certified corpus of 2,937 elliptic curves (63 quarantined against pre-declared tripwires) with full provenance, each carrying verifiable L-polynomial, rank, ε-sign, |Sha|, and per-place traces; (2) a two-witness certificate pipeline (CERT_SCHEMA v0) with explicit certificate classes (TIER A computed-two-witness / TIER B theorem-formula), whose upper witness is validated on 5 of 5 rank-2 specimens in controls-first mode — including disclosure of a caught-and-halted pipeline defect; and (3) a calibrated murmuration detection at certified scale — pooling the degree-5 block (n = 557), the rank-0/rank-1 contrast reaches z = +2.69 at place degree d = 2 under a 10⁴ label-permutation null (p = 0.007, Bonferroni ×4 = 0.028). Detection, not replication, is claimed — the pre-registered z ≥ 15 replication bar was not met (n ≈ 10³ vs 5·10⁵). A Kummer/Ulmer tower (Conceição–Hall–Ulmer, MRL 2014) supplies a TIER B theorem-formula truth base reaching rank 59,048 (declared independence limitation: witnesses share a theorem). Limits: ℚ-transfer is H0 (AUC 0.5451 ≤ 0.55); in-family machine learning is screening only; falsification criteria are stated explicitly in the paper. All numbers trace to hash-committed artifacts. Keywords: elliptic curves; function fields; Birch–Swinnerton-Dyer; murmurations; certification.