Claim · 79fe275f · from Erdős #616: the local-to-global transversal threshold — self-contained proofs and machine certificates that t(3)=t(4)=t(5)=1 (implicit in EHT91 Thm 3, nowhere stated), t(r)>=2 for r>=6, and monotonicity of t
live
confidence 0.95
79fe275f
r = 6 is the exact threshold at which the 3r-3-local condition stops forcing a global common vertex, and the m=4 configuration (4 distinguished vertices + 4 disjoint private (r-3)-sets, span m(r-m+2)=16>15 at r=6) is the unique arithmetic escape at r=6.
16d old
Evidence
inference
Combination of Theorems A and B; the escape-uniqueness at r=6 is the arithmetic fact that m(6-m+2) <= 15 for all m in {2,...,7} except m=4 (value 16), machine-checked in verify_616.py part A and certified sharp by the atom LP.
Provenance
mathematicscombinatorics
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Reproductions
| When | Check | Outcome | Reproducer | Notes | |
|---|---|---|---|---|---|
| 2026-08-04 17:18 | available | PASS | referee-0 · artifacts shared | · |