Shannon capacity of the 7-cycle

Upper bound, last-listed row

| $\vartheta({\mathcal C}\_{7}) \approx 3.3177$ | [L1979] | Lovász theta-function bound |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $3.25883262\ldots$ | [Tan2026] | Heterogeneous recursion; independent set in ${\mathcal C}\_{7}^{\boxtimes 500}$. Certificates: https://github.com/tandonravi/C7-Shannon-Capacity-Heterogeneous-Recursion |value changed 2026-09-26

Checked against material for its cited source

• Another row, not one shown above: bound row $367^{1/5} \approx 3.2578$ line 40 citing [PS2018] — the claim we checked: that the cited paper gives an independent set of size 367 in the fifth strong power of the 7-cycle, from which the row's value, the fifth root of 367 (≈ 3.2578), follows by arithmetic. The journal's accepted manuscript and the arXiv preprint both support it; the typeset journal pages the entry cites could not be reached, so whether they say the same is not settled. This verdict does not cover whether the 367 listed words really form an independent set; they were not checked. source link (reached in two editions other than the typeset Information Processing Letters pages the entry cites: the journal's accepted manuscript for that article (Elsevier PII S0020-0190(18)30229-1, an "unedited manuscript" before copyediting, from the CWI repository, ir.cwi.nl/pub/30364), its cover, highlights and manuscript pp. 1–5, and arXiv:1808.07438 v2, pp. 1–5, both read from page images. The typeset journal pages were not reached). Selected: drawn by its position in the list of cited rows, not because it looked wrong.

1 bound row(s) here have been checked against material for their cited source (1 drawn by position, 0 chosen because something already looked wrong). Across this whole ledger 70 row(s) have been drawn by position, against 691 rows that name a source, counted on 2026-09-27: 64 were checked against material for their cited sources and for 6 the cited source could not be read at all. 5 more were chosen for suspicion and checked; they are counted apart, because a set selected for suspicion carries no rate. A row not listed here has NOT been checked.