Designing Anti-Tautological Probes on the 6N Skeleton: A Negative Case Study with Elliptic-Curve Ranks and the CRT Information Barrier

This note is methodological, not a claim of new arithmetic. Within the heuristic "6N" framework (primes greater than 3 lie on the residue classes 6N±1), we ask whether the 6N wing of a prime p exerts any control over a high-dimensional arithmetic invariant attached to p: the Mordell–Weil rank of the elliptic curve E_p : y² = x³ − p. We first articulate a discipline for distinguishing genuine probes from tautological ones — probes whose observable is a re-encoding of primality — and argue that the rank of E_p is the one clean, primality-independent observable with a natural 6N bridge (p mod 6). Using certified true ranks for the 1116 of 1227 curves with p < 10⁴ computable to certainty (SageMath), a three-layer analysis (raw wing effect; effect within fixed root-number classes; label-shuffle null) finds no wing control of rank: Cohen's d = +0.022 raw, d ≈ +0.02 within both root-number classes, and a shuffle test yielding p = 0.913. Rank is organized entirely by the root number (a function of p mod 24). We interpret this as a concrete instance of a Chinese-Remainder information barrier: 6N is a mod-6 datum and is, by the CRT factorisation of the relevant conductor/root-number data, absorbed by the finer mod-24 structure that governs the invariant. The contribution is the falsification discipline and a worked, honestly-negative example — not a new theorem.