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31a: note that the 0.79970 lower-bound row is a Monte Carlo/Hoeffding estimate - #265
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…estimate The [AA2026] row comes from the mean of a beam-search heuristic over 10^6 random string pairs minus a Hoeffding margin with delta = 1e-12 (method as stated in its README). It therefore holds with probability 1 - 1e-12 over the sample and is not a deterministic lower bound. Comment only, no value or asterisk changed. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Comment-only change to the 31a lower-bound row$0.79970$ * [AA2026]. The value and the asterisk are unchanged.
The [AA2026] repository describes its method as "Monte Carlo beam search + Hoeffding". The mean length of a width-100 beam-search common subsequence over$M = 10^6$ random pairs of length-1000 binary strings is 0.803417, and Hoeffding's inequality with $\delta = 10^{-12}$ subtracts 0.003717. So the statement holds with probability $1 - 10^{-12}$ over the sampled strings. It isn't a deterministic bound: a rigorous version would need the exact expectation of the heuristic at $N = 1000$ . This PR just says so in the Comments cell, so readers can tell it apart from the exact finite-state bounds (Lueker; Heineman et al., 0.792665992). Whether the row should stay in the Bound column is your call.
I noticed this while independently replaying the C_31 upper bounds, which #249 already covers.
Prepared with Claude Code (Anthropic), from the [AA2026] README. Noted in the page's Contribution notes.
🤖 Generated with Claude Code