Certified computational record table: for every totient value a ≤ A_max = 30,641,761,281 the exact minimal preimage f(a) is determined (sieve over n ≤ 1.94×10^11 plus an elementary completeness lemma guaranteeing all preimages of such a lie ≤ N). There are 3,903,102,222 totient values ≤ A_max; exactly 31,043 of them have f(a)/a ≥ 2 (complete census; a further 3,408,149 have 1.9 ≤ ratio < 2); the maximum ratio is 2.043447, attained at a=387383296=2^16·23·257 with f(a)=791597265=3·5·17·47·257²; no totient value a ≤ 3.06×10^10 has f(a)/a ≥ 2.05. The running-record positions are exactly 2, 8, 128, 5888, 2037248, 387383296, reproducing OEIS A393265 independently and certifying the list's completeness for a ≤ 3.06×10^10. Census structure: 31,029 of the 31,043 have ODD minimal preimage (all built from the Fermat kit 3·5·17(·257) with Sophie-Germain-type carriers, e.g. every top-16 record has f(a)=3·5·17·47·347·q or 3·5·17·47·257²); the 14 even ones include a=2^32, 2^33, 2^34 with ratio exactly 2 — the sieve independently exhibits Theorem 1's family in range; minimum v₂(a) over the census is 8.