| Lifting relations over an Artinian base | statement | lemma 18.6 | arxiv |
| Exact rank-one-link component | statement | proposition 4.3 | arxiv |
| The quotient by the primary image | statement | corollary 17.6 | arxiv |
| Complete next-to-top strand | statement | corollary 7.2 | arxiv |
| Complete hyperplane-graph formula | statement | theorem 1.2 | arxiv |
| Graphic matroids | statement | corollary 9.1 | arxiv |
| Direct-sum additivity | statement | corollary 11.5 | arxiv |
| Polynomial gap | statement | lemma 15.4 | arxiv |
| Direct sums | statement | corollary 6.6 | arxiv |
| Smoothness dichotomy | statement | corollary 8.8 | arxiv |
| Realization in every negative component | statement | theorem 18.4 | arxiv |
| Complete rank-three degree-zero formula | statement | theorem 13.1 | arxiv |
| Sharp uniform bounds | statement | corollary 6.5 | arxiv |
| Reconstruction of large cocircuits | statement | theorem 6.8 | arxiv |
| Cographic matroids | statement | corollary 9.2 | arxiv |
| Universal pure-pair cup product | statement | theorem 1.4 | arxiv |
| Sharp rank-three extremum | statement | theorem 15.6 | arxiv |
| The quotient missed by the primary cup | statement | proposition 18.3 | arxiv |
| Graded polarization of the primary obstruction | statement | lemma 8.6 | arxiv |
| Complete fine Hilbert series | statement | corollary 3.3 | arxiv |
| Long-line point bound | statement | lemma 15.2 | arxiv |
| Rank-word transform for the cocircuit profile | statement | theorem 16.1 | arxiv |
| Universal hyperplane-graph formula | statement | theorem 3.1 | arxiv |
| Actual quadratic obstructions | statement | corollary 8.7 | arxiv |
| Standard-degree-zero master formula | statement | theorem 12.1 | arxiv |
| Tutte contrast | statement | theorem 6.7 | arxiv |
| Unbounded obstruction order at corank three | statement | theorem 1.1 | arxiv |
| Smoothness dichotomy | statement | corollary 1.6 | arxiv |
| Vanishing and the excluded minor | statement | theorem 1.3 | arxiv |
| A5HHJ9SGY5 | statement | corollary 5.5 | arxiv |
| The primary image in every fine degree | statement | theorem 17.5 | arxiv |
| Trichotomy for the hyperplane graphs | statement | lemma 17.1 | arxiv |
| Finite compatibility table | statement | lemma 15.5 | arxiv |
| Rank-two pure-pair rank | statement | corollary 11.6 | arxiv |
| Graded smoothness dichotomy | statement | corollary 8.9 | arxiv |
| Rank-three obstruction rigidity | statement | theorem 14.2 | arxiv |
| The boundary of valuativity | statement | proposition 16.3 | arxiv |
| Sharp rank-two extremum | statement | theorem 10.2 | arxiv |
| Cyclic higher obstruction | statement | theorem 18.1 | arxiv |
| Explicit inverse algorithm | statement | corollary 14.3 | arxiv |
| Valuative rank-one obstruction series | statement | corollary 16.2 | arxiv |
| Nonzero standard-degree-zero cup product | statement | theorem 8.5 | arxiv |
| Realization of the homogeneous primary quotient | statement | theorem 18.7 | arxiv |
| Circuit profile and basis average | statement | theorem 6.4 | arxiv |
| Uniform rank three | statement | corollary 13.2 | arxiv |
| Exact stability gap | statement | corollary 11.8 | arxiv |
| A bipartite graph lemma | statement | lemma 5.1 | arxiv |
| Finite detector | statement | corollary 6.2 | arxiv |
| Localization and cup products | statement | lemma 2.1 | arxiv |
| Rank-three stability | statement | corollary 15.7 | arxiv |
| Purely negative $T^2$ in rank two | statement | theorem 7.1 | arxiv |
| Global pure-pair obstruction rank | statement | theorem 11.4 | arxiv |
| The purely negative primary image | statement | theorem 17.3 | arxiv |
| Field-independent coordinate formula | statement | lemma 8.1 | arxiv |
| Constructive large-cocircuit lemma | statement | theorem 5.3 | arxiv |
| Rank-two reduction | statement | proposition 5.2 | arxiv |
| Linear arcs and exact quadratic obstructions | statement | theorem 8.11 | arxiv |
| Generation of first cohomology | statement | lemma 17.4 | arxiv |
| Unimodularity and absence of bad primes | statement | corollary 11.2 | arxiv |
| Small-complement cases | statement | lemma 15.3 | arxiv |
| Rank-two closed form | statement | proposition 10.1 | arxiv |
| Pure-pair obstruction ranks | definition | definition 11.3 | arxiv |
| Vanishing classification | statement | theorem 5.4 | arxiv |
| Two-element block formula | statement | corollary 4.1 | arxiv |
| Rank-two negative support | statement | theorem 17.2 | arxiv |
| Cocircuit reconstruction | statement | theorem 14.1 | arxiv |
| The Fano plane | statement | corollary 13.3 | arxiv |
| One contraction retaining large corank | statement | lemma 8.4 | arxiv |
| Finite coefficient algorithm | statement | corollary 12.2 | arxiv |
| Graded uniqueness of the realizing jets | statement | corollary 18.5 | arxiv |
| Universal pure-pair surjectivity | statement | theorem 8.2 | arxiv |
| Generators, relations, and support of the primary quotient | statement | theorem 18.8 | arxiv |
| Integral pure-pair obstruction lattice | statement | theorem 11.1 | arxiv |
| Projective planes | statement | corollary 7.3 | arxiv |
| Fine and coarse series | statement | corollary 6.3 | arxiv |
| Closure-stratified series | statement | corollary 3.4 | arxiv |
| Purely negative cocircuit witnesses | statement | proposition 4.2 | arxiv |
| Zero-dimensional calculation | statement | lemma 2.2 | arxiv |
| Link-lifted cup products | statement | corollary 8.3 | arxiv |
| Sharp rank-two pure-pair extremum | statement | theorem 11.7 | arxiv |
| Pencil concentration bound | statement | lemma 15.1 | arxiv |
| A six-element cubic obstruction | example | example 18.2 | arxiv |
| Degree-zero obstructions in every rank | statement | theorem 1.5 | arxiv |
| Complete rank-one-link strand | statement | theorem 6.1 | arxiv |
