1) V1 If f(n) is the number of distinct sets of cycle lengths realized by simple graphs on n vertices, then f(n)/2^(n/2) tends to infinity.
open, filed Tue Aug 25 2026 06:20:30 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Six-role fleet passed. Independent definitions agree both ways; Set.finite_range proves ncard is genuine finite counting; cycleGraph 3 is detected while length 2 is impossible; false-premise control preflights red/restatement; negation is exactly the open limit; literature confirms only the upper-density half is solved; final Jig dedupe is empty. Whole attacks tested multi-fan encodings, lower-cycle tags, disjoint gadget products, container-bound reversal, and refutation by O(2^(n/2)); every route hits collision or vertex-budget barriers. No cosmetic partial filed.
Scope. All finite undirected simple graphs on exactly n labeled vertices; spectra are deduplicated as sets of natural cycle lengths; only the remaining open lower-growth claim, not the solved o(2^n) claim.