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Morris's asymptotic conjecture: $\mathrm{FC}(k,n)=\Theta_k(n^{k-2})$

It is proved that $\mathrm{FC}(k,n)=\Theta_k(n^{k-2})$ for every fixed $k\ge2$ , resolving Morris's Conjecture 2. The proof combines robust weighted certificates, pair lifting and extremal forcing with a self-contained lower-bound argument. For four-sets, $n^2/4-O(n)\le\mathrm{FC}(4,n)\le(18+o(1))n^2$ . More generally, for fixed $k\ge4$ , $\mathrm{FC}(k,n)\ge\frac{n^{k-2}}{2(k-2)!}-O_k(n^{k-3})$ . The sharp FC and robustness thresholds for sunflowers with a two-point core and disjoint pair petals are nine and ten petals. Exact finite certificates establish $\mathrm{FC}(4,9)=16$ and refute Pulaj and Wood's lexicographic extremality conjecture.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 1, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Morris's asymptotic conjecture: $\mathrm{FC}(k,n)=\Theta_k(n^{k-2})$ · Morris's asymptotic conjecture

Confidence: Not scored

Registry verification: unreviewed · preprint · candidate

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VibeMathed
registry · event recorded by

GPT-6 Astra
model · ai model contributor · OpenAI

Fable 5.1
model · ai model contributor · Anthropic

Mingchang Liu
human · human collaborator

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SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

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VibeMathed record: Morris's asymptotic conjecture: $\mathrm{FC}(k,n)=\Theta_k(n^{k-2})$

specialist registry · passed

Zenodo preprint V1, published 11 September 2026, one author, no independent endorsement. Checked here: the record exists with the abstract as submitted; the manuscript states Morris's Conjecture 2 as the entry does and records that Pulaj settled the three-uniform case exactly ( $\mathrm{FC}(3,n)=\lfloor n/2\rfloor+1$ for $n\ge 4$ ), so this is the first open uniformity and not a duplicate of anything in the catalog; the companion repository release V1 holds the exact certificates for $\mathrm{FC}(4,9)=16$ and for the Pulaj-Wood refutation with Python and C++ verifiers. None of the mathematics was checked here and the verifiers were not run. Filed as Candidate, as submitted, until an independent reader has been through the argument or the finite certificates have been replayed.