| 1QJ5H4CR8P | statement | corollary 2.9 | arxiv |
| the chordless four-cycle | example | example D.11 | arxiv |
| exact cell counts | statement | proposition 8.3 | arxiv |
| CW realization of coherent permuted gluings | statement | proposition E.4 | arxiv |
| closed-cell reduction | statement | lemma 6.2 | arxiv |
| the $2$-skeleton does not determine a quotient flag complex either | statement | proposition 2.7 | arxiv |
| flag case: regularity is visible on edges | statement | corollary 6.5 | arxiv |
| A permutation quotient outside the unchanged semisimplicial inventory | statement | proposition E.5 | arxiv |
| the cone model | definition | definition 8.1 | arxiv |
| skips are hollow simplices | statement | lemma 4.1 | arxiv |
| locality of the collapse | statement | proposition 9.1 | arxiv |
| vertex-minimality | statement | theorem A.3 | arxiv |
| classes created by a flag collapse | statement | theorem 2.11 | arxiv |
| strict hierarchy | statement | proposition D.7 | arxiv |
| $m$-flag | definition | definition C.1 | arxiv |
| pointed face presentations | definition | definition 3.3 | arxiv |
| regularity implies strict gradedness | statement | proposition 6.6 | arxiv |
| basepoint chains | definition | definition 3.2 | arxiv |
| codimension-one constructibility | statement | corollary 3.13 | arxiv |
| normalized relative chains | definition | definition 3.14 | arxiv |
| disjoint faces can be crushed without changing the ball pair | statement | lemma 6.3 | arxiv |
| quotient towers | statement | proposition 3.17 | arxiv |
| Torus | example | example E.10 | arxiv |
| forcing, graded | statement | lemma C.4 | arxiv |
| truncated storage | statement | corollary 5.7 | arxiv |
| E4QXH6P5B3 | statement | lemma 2.3 | arxiv |
| absolute and relative quotient homology | statement | corollary 2.10 | arxiv |
| categories of pairs | definition | definition 3.9 | arxiv |
| intrinsic forcing | statement | lemma C.7 | arxiv |
| Notation | definition | definition 2.5 | arxiv |
| G7SJVYS9Y5 | statement | proposition 2.8 | arxiv |
| Signed cover categories and their morphisms | definition | definition B.1 | arxiv |
| labelled, dimension-bounded | statement | proposition C.6 | arxiv |
| gluings are determined by no finite skeleton | statement | proposition 5.8 | arxiv |
| joins | statement | lemma A.1 | arxiv |
| iterated faces | definition | definition D.5 | arxiv |
| relative and absolute cellular chains | statement | theorem 3.15 | arxiv |
| cells of the pointed realization | statement | lemma 3.6 | arxiv |
| component-resolved shallowness | definition | definition 3.7 | arxiv |
| the low-degree correction | example | example 3.16 | arxiv |
| coherent gluing datum with permutations | definition | definition E.3 | arxiv |
| simplex quotients | statement | corollary D.2 | arxiv |
| facet budget, graded | statement | lemma C.3 | arxiv |
| when the cone model stays flag | statement | proposition 8.2 | arxiv |
| A free-cover nerve is not a realization | statement | proposition B.8 | arxiv |
| Signed cover data lose attachment information | statement | proposition B.10 | arxiv |
| P0JFTENXER | definition | definition 6.1 | arxiv |
| order-preserving gluing datum | definition | definition E.1 | arxiv |
| the $1$-skeleton does not determine a quotient flag complex | statement | proposition 2.6 | arxiv |
| Q56S5VK875 | statement | lemma 2.2 | arxiv |
| The free-cover nerve is a graph up to homotopy | statement | proposition B.9 | arxiv |
| $m$-flag collapses are $(2m{+}1)$-determined | statement | theorem 5.4 | arxiv |
| pointed realization | definition | definition 3.5 | arxiv |
| embedding criterion for the inherited maps | statement | proposition D.6 | arxiv |
| QPPW3QMWYK | definition | definition 2.1 | arxiv |
| realization | statement | theorem 3.11 | arxiv |
| full-component criterion | statement | theorem 6.4 | arxiv |
| Cover functor | definition | definition B.3 | arxiv |
| all-cell acyclicity | statement | corollary D.3 | arxiv |
| graded strictness | statement | theorem C.5 | arxiv |
| why the edge test needs flagness | example | example D.12 | arxiv |
| sharpness | statement | proposition 5.6 | arxiv |
| Properties of the cover functor | statement | proposition B.4 | arxiv |
| where a cover can skip rank | statement | lemma 3.8 | arxiv |
| a collapsible boundary arc: a ball with irregular cells | example | example D.9 | arxiv |
| strict gradedness for flag ambient complexes | statement | theorem 4.2 | arxiv |
| two opposite edges of a tetrahedron | example | example D.10 | arxiv |
| unified threshold for flag ambient complexes | statement | theorem 5.5 | arxiv |
| M\"obius band and $\mathbb{RP}^2$; a doubled cover | example | example E.12 | arxiv |
| Lens spaces on one source, with distinct attaching data | example | example E.9 | arxiv |
| flag collapses are labelled $3$-determined | statement | proposition 5.3 | arxiv |
| unravelling the presentation | statement | lemma 3.4 | arxiv |
| W936DKBR95 | statement | theorem A.2 | arxiv |
| decoration | definition | definition 3.10 | arxiv |
| Compatible orders for cyclic bipyramid gluings | statement | proposition E.7 | arxiv |
| WXG1SDTWME | definition | definition C.2 | arxiv |
| Linearization of covers | definition | definition B.5 | arxiv |
| facet budget | statement | lemma 5.2 | arxiv |
| forcing | statement | lemma 5.1 | arxiv |
| one edge of a triangle: regular cells, non-embedded source maps | example | example D.8 | arxiv |
| Componentwise collapse | definition | definition 2.4 | arxiv |
| the extremal collapse family | example | example A.5 | arxiv |
