Constants checked tonight

object	value	published	tonight
$T$	$\delta=1/3$ , $e=3$	Kislitsyn / Aigner	same, two counters
Saks $M_7$	$\delta=14/39$ , $e=39$	Saks 1985	down `[0,0,1,1,7,7,31]`, pair $25:14$
Chen $P(5,5)$	$\delta=37/106$ , $e=106$	Chen 2018; Olson–Sagan $C$	same
width-3 min, $n\le 9$	$14/39$	TGF 1992; Olson–Sagan 2018	0 exceptions in 11,026,537 width-3 natural labellings at $n=9$
width-3 min, $n=10$	$6/17$	unpublished	$W_{10}$ , $e=187$ , pair $121:66$ , unique unlabelled
$6/17$ vs $14/39$	$6/17 < 14/39$	—	$6\cdot 39=234 < 17\cdot 14=238$
$C_2\times C_6\times C_3$	$\delta\approx 0.480377$	—	exact $273419876590786707/569177957111013830$

BFT general bound $(5-\sqrt5)/10$ is untouched. Width-2 records (Chen $\kappa\approx 0.3489$ , Olson $37/106$ ) are untouched.

2026-08-27

Gupta v2 named witnesses, this notebook's counters:

Broken-rung non-sum minima $7\le n\le 21$ are in q1/ladder_census.json. No width-3 one-point extension of $W_{10}$ has $\delta<6/17$ .

object	value
$L_{22,1,5,6,9,12,13,17}$	$\delta=1065/3049$ , $e=54882$
three-rail $n=15$ min	$30572/78185$ , width 3, $2{,}097{,}152$ non-sums
interval orders $n\le 10$	min $\delta=1/3$ ; non-semiorder min $8/21$ then $47/130$ ; A367494 match

No $\delta<1/3$ . No width-3 three-rail example below $6/17$ . Tables in q2/.