Probable Dipole of the NIR-H Flux Tail Index in the Euclid MER Q1 Public Release: A Robust Empirical Detection over a Narrow Longitudinal Band

This paper reports a statistically robust North–South asymmetry of the heavy-tail index of the NIR-H flux distribution (Sersic H-band flux) in the Euclid Multi-Epoch Release Q1 public catalogue, accessed via ESASky 7.40. Using the Hill estimator with threshold k = 50, declared prior to any analysis, applied to five independent sky zones covering declinations δ ≈ +60° and δ ≈ −26° to −50°, we measure a block-averaged contrast Δα ≈ 0.80 between North zones (ā_N ≈ 2.01) and South zones (ā_S ≈ 1.21). The minimum North value exceeds the maximum South value by 0.629, yielding a near-total group separation. The contrast persists under all robustness tests: k-stability (<10% variation over k ∈ [40; 90]), bootstrap (B=1000, P(Δα > 0) ≈ 0.996), leave-one-out (0.67 ≤ Δα ≤ 0.93), KS test (D = 0.083, p < 10⁻⁶), and variance inflation (Z > 1.6 with tripled variance). No cosmological interpretation is imposed. The result is conservatively interpreted as a probable large-scale dipole precursor, testable with Euclid Q2/Q3 public data expected in October 2026. Full methodological transparency and zero free parameters. File integrity (SHA-256) :EN : DB212AB024FF7C90AE8D93472AE45812A60F57F56662904DF7CE9776E9276EC5