When the Ring Breaks Symmetry: Closure-Only Harmonic Validation and a Z3 Residual Transient in M87 (EHT 2017, MJD 57848)

We present a closure-phase–only, cross-pipeline analysis designed to separate robust, global source structure from overfit high-order artifacts in interferometric data. Using M87 observations from 2017-04-05 (MJD 57848) reduced independently with two pipelines (HOPS and CASA), and in two contemporaneous frequency bands (HI and LO), we test a sequence of azimuthal harmonic ring models parameterized by a ring scale (R, w) and a harmonic set M ⊂ {0, 8, 16, 24}. The key methodological choice is to evaluate all models with a closure-only likelihood and to perform model comparison on unseen data via a strict train/test split. We report test-set ΔBIC values (negative favoring the alternative) that decisively support adding m = 8 to an axisymmetric baseline m = 0 in all four data partitions, establishing m = 8 as a stable, repeatable component. In contrast, adding m = 24 on top of a locked baseline (m = 0, 8, 16) yields mixed outcomes, including a strongly positive ΔBIC in HOPS_HI, demonstrating that a static, global m = 24 component is not uniformly supported and is susceptible to overfitting in full-track fits. Motivated by a phenomenological “unlocking” map in which the relative amplitude A24/A8 remains intrinsically small (≤ 0.058 even at full unlock), we pivot to time-localized detection. We introduce a Z3 proxy statistic computed from baseline-subtracted closure-phase residuals, Z3 = ⟨exp(i·3·Δψ)⟩, whose magnitude S3 = |Z3| quantifies threefold phase coherence expected when the m = 24 contribution becomes temporarily coherent relative to the locked modes. A permutation test over shuffled time labels (up to 2000 trials) finds highly significant max-bin events within each dataset (typical p_max = 5×10⁻⁴) and strong agreement between HI/LO within each pipeline. We further verify that there is no timestamp mismatch between pipelines (median raw-time offset 0 hr). The previously observed ~1 hour separation between binned peaks is shown to be an estimator and bin-origin effect rather than a clock offset. To remove bin-edge sensitivity, we compute a Gaussian-kernel sliding-window residual statistic S3,res(t), obtaining broad, overlapping high-coherence plateaus across all four datasets in the interval ~05:40–07:10 UTC, with peaks clustered near 06:00–07:08 UTC depending on pipeline and band. Overall, the evidence supports a clear dichotomy: low-order harmonics (m = 8, 16) behave as locked global structure, while the m = 24 signature is inconsistent with a static component but is consistent with a transient episode detected robustly in closure-only residual coherence across independent reductions.