Iteration 73 — H-038 Energy Distance Passes the Exam EXAM PASS · DERIVED EXACTNESS HELD · GROUPED COUSINS M3 NEXT

In plain words: the second distance cousin — a distribution-difference meter built from plain absolute differences, with NO tuning knobs at all (no kernel, no bandwidth) — passed its exam on the first form, and with a methodological first for the campaign: after two exams whose "must read exactly X" claims broke on floating-point technicalities, this one's exactness claim was DERIVED before running (all three terms flow through one shared code path; doubling is exact in binary arithmetic; equals-minus-equals is exactly zero) — and the machine then read exactly 0.0, as proven. On real regime pairs it sees separations at 3 to 31 times its shuffle bar. Now comes the fight it was warned about at the door: energy distance is mathematically an MMD in disguise, and the gambler died last week for exactly that kinship. Next firing runs the economical version of that fight — one census computing BOTH remaining cousins (this one and the transport-geometry one), both judged against certificate #13's shadow in the same run. Two kills would close the distance family for good; any survivor must show its geometry genuinely reads a different ranking.