| Structure of the design code as a $G$-module | statement | theorem 3.28 | arxiv |
| Three-subsets fixed by a permutation | statement | lemma 2.66 | arxiv |
| Basic counting | statement | lemma 2.1 | arxiv |
| Framework for $HS$ and $Co_3$ | statement | theorem 2.85 | arxiv |
| Extension lemma | statement | lemma 2.90 | arxiv |
| Outer extensions: general reduction | statement | proposition 2.91 | arxiv |
| Block-transitive triple systems | statement | corollary 3.1 | arxiv |
| Designs from $\PSL(2,q)$ | statement | corollary 2.20 | arxiv |
| Spectrum and structure of the incidence graph | statement | theorem 3.6 | arxiv |
| Ree extension: reduction to socle orbits | statement | theorem 2.80 | arxiv |
| Classification of the binary orbit codes | statement | corollary 3.20 | arxiv |
| Dihedral two-point stabilizer and its suborbits | statement | lemma 2.68 | arxiv |
| 53DT4Q44A0 | statement | corollary 2.82 | arxiv |
| Extension formula for every field quotient | statement | proposition 2.77 | arxiv |
| Collinear triples | statement | theorem 2.104 | arxiv |
| Computed affine case: $\SL(2,13)\le\GL(6,3)$ | statement | proposition 2.107 | arxiv |
| The even-$d=3$ unitary case: closed forms | statement | proposition 2.40 | arxiv |
| Trivial pointwise stabilizers of non-collinear triples | statement | lemma 2.38 | arxiv |
| Diagonal-overgroup orbit number of $\PGU(3,q)$ | statement | proposition 2.36 | arxiv |
| Ree reduction | statement | theorem 2.63 | arxiv |
| Main classification | statement | theorem 1.1 | arxiv |
| Flag-transitive triple systems | statement | corollary 3.2 | arxiv |
| Designs from $\Ree(q)$ | statement | corollary 2.72 | arxiv |
| Pointwise stabilizers of non-collinear triples | statement | lemma 2.67 | arxiv |
| Fixed orbits carry the full $S_3$ image | statement | lemma 2.41 | arxiv |
| 8BJSRFGGFR | definition | definition 3.18 | arxiv |
| $\AaL(1,p^d)$ | statement | theorem 2.98 | arxiv |
| Overgroups of $\PSU(3,q)$ | statement | theorem 2.48 | arxiv |
| Exceptional affine cases | statement | theorem 2.105 | arxiv |
| Designs from $\Sp(2n,2)$ | statement | corollary 2.28 | arxiv |
| Counting of transpositions and $3$-cycles | statement | lemma 2.70 | arxiv |
| Optimal Steiner orbit codes | example | example 3.22 | arxiv |
| Orbits on triples from the two-point stabilizer | statement | proposition 2.12 | arxiv |
| Three-point stabilizers for the Suzuki group | statement | theorem 2.53 | arxiv |
| Three-subset orbit structure of $\Ree(q)$ | statement | theorem 2.71 | arxiv |
| Field overgroups not containing $\PGL(2,q)$ | statement | theorem 2.24 | arxiv |
| Well-definedness of the square-class invariant | statement | lemma 2.16 | arxiv |
| Determinant of the twisted correction | statement | lemma 2.23 | arxiv |
| Classification of the $2$-homogeneous groups | statement | lemma 2.109 | arxiv |
| Class number and valencies | statement | proposition 3.31 | arxiv |
| Computational reduction of the intersection numbers | statement | proposition 3.33 | arxiv |
| Orbital graph criteria | statement | lemma 3.4 | arxiv |
| Field-automorphism extensions of $\Ree(q)$ of cubic degree | statement | theorem 2.74 | arxiv |
| Computed Suzuki cases | statement | proposition 2.61 | arxiv |
| Minimum distance of orbit codes | statement | theorem 3.19 | arxiv |
| Computed stabilizer refinement for $q\le49$ | statement | proposition 2.43 | arxiv |
| Designs from $\Sz(q)$ | statement | corollary 2.55 | arxiv |
| Geometry of the unital | statement | lemma 2.32 | arxiv |
| Arc-transitivity via the stabilizer image | statement | proposition 3.10 | arxiv |
| Summary of the almost simple analysis | statement | theorem 2.92 | arxiv |
| Arc-transitivity criterion | statement | theorem 3.8 | arxiv |
| All-ones word and the dual code | statement | proposition 3.26 | arxiv |
| Ree extension: orbit reduction | statement | proposition 2.79 | arxiv |
| HZD93EQNKW | statement | theorem 2.83 | arxiv |
| Strong regularity of the block graph | statement | proposition 3.15 | arxiv |
| Rank, all-ones word, self-orthogonality | statement | theorem 3.24 | arxiv |
| Steiner orbit codes meet the Johnson bound | statement | theorem 3.21 | arxiv |
| $\PSL(2,q)$: three-point stabilizers | statement | theorem 2.17 | arxiv |
| The sporadic group $Co_3$ on $276$ points | statement | proposition 2.89 | arxiv |
| The overgroup $HS.2$ on 176 points | statement | proposition 2.88 | arxiv |
| The three-point stabilizer in affine groups | statement | lemma 2.93 | arxiv |
| P017STHPCC | example | example 3.16 | arxiv |
| Block graph: general and Steiner cases | statement | theorem 3.13 | arxiv |
| Unitary two-point suborbits and the three-point orbit number | statement | theorem 2.35 | arxiv |
| Full rank and minimum weight of the unitary design codes | statement | proposition 3.25 | arxiv |
| Numerical class numbers (computed | statement | proposition 3.34 | arxiv |
| Designs from $\PSL(n,q)$ on projective space | statement | corollary 2.27 | arxiv |
| Small-parameter verification for $\PSL(n,q)$ on projective space | statement | proposition 2.26 | arxiv |
| The odd-$d=3$ unitary case: closed forms | statement | proposition 2.42 | arxiv |
| Every orbit is a triple system | statement | proposition 2.3 | arxiv |
| Unions of orbits are triple systems | statement | proposition 2.4 | arxiv |
| Non-collinear triples | statement | theorem 2.101 | arxiv |
| Design parameters for the unitary family | statement | corollary 2.47 | arxiv |
| RB2ZWZM2RD | example | example 2.100 | arxiv |
| Fixed orbits for the cubic field extension | statement | lemma 2.73 | arxiv |
| All $G$-invariant triple systems | statement | corollary 2.5 | arxiv |
| $\AGL(1,p^d)$ | statement | theorem 2.96 | arxiv |
| Orbit triple system | definition | definition 2.2 | arxiv |
| Three-subset orbits of $\Sp(2n,2)$ | statement | theorem 2.30 | arxiv |
| The smallest Ree instance $q=3$ | example | example 2.62 | arxiv |
| The field conjugation causes no fusion for general $q$ | statement | proposition 2.49 | arxiv |
| Collinear triples | statement | theorem 2.33 | arxiv |
| Ree class input | statement | lemma 2.65 | arxiv |
| Suzuki field extensions: reduction | statement | theorem 2.57 | arxiv |
| The complete finite-field count | statement | lemma 2.58 | arxiv |
| Schurian coherent configuration on triples | definition | definition 3.30 | arxiv |
| V533V2ZFXS | statement | proposition 3.11 | arxiv |
| Suborbit reduction | statement | lemma 2.11 | arxiv |
| Galois descent and the fixed-orbit count for the Ree socle | statement | proposition 2.75 | arxiv |
| Orbit data of the square-subgroup affine group | statement | theorem 2.110 | arxiv |
| The Suzuki orbit number | statement | theorem 2.54 | arxiv |
| The $C_3$-criterion on the unital | statement | lemma 2.39 | arxiv |
| WQCVVZR2HH | definition | definition 3.5 | arxiv |
| WRDJH976Y6 | statement | theorem 2.81 | arxiv |
| Three-point stabilizers in $\PSL(n,q)$ on projective space | statement | theorem 2.25 | arxiv |
| X2WC7AQSAA | definition | definition 3.23 | arxiv |
| Classification of finite $2$-transitive groups | statement | theorem 2.8 | arxiv |
| The $G_2'$ rows: orbits and pointwise stabilizers | statement | theorem 2.103 | arxiv |
| Three-subset orbits of Suzuki field extensions | statement | theorem 2.59 | arxiv |
| Orbit fusion under a normal subgroup | statement | lemma 2.15 | arxiv |
| Three-subset orbit number of $\Ree(q)$ | statement | theorem 2.69 | arxiv |
| $\PGL(2,q)$, $\PpGL(2,q)$ | statement | theorem 2.21 | arxiv |
| Arc-transitive families | statement | corollary 3.9 | arxiv |
