| The $A_-$ classes stratify, and the degeneration is local | statement | fact 11.9 | arxiv |
| The unitary partner of the diagonal words | statement | corollary 19.6 | arxiv |
| The $A_-$ spins at $L^3R^3$ | statement | fact 20.1 | arxiv |
| The flat directions are chain shifts | statement | proposition 15.1 | arxiv |
| The kernel vector and spin of an $A_-$ class | statement | theorem 14.1 | arxiv |
| Arc-continuant lemma | statement | lemma G.1 | arxiv |
| The universal Floquet vector | statement | lemma B.2 | arxiv |
| Sine triples | statement | lemma 12.2 | arxiv |
| The base-vacuum rule: the spin modulo $1$ | statement | fact 11.8 | arxiv |
| 43CHDE0KN6 | definition | definition | arxiv |
| The $\mathcal H$-spectrum of $L^mR^m$ | statement | proposition 11.1 | arxiv |
| Existence | statement | theorem 16.1 | arxiv |
| 4XRA74SJFB | statement | proposition 12.5 | arxiv |
| Life of an edge | statement | lemma A.1 | arxiv |
| The frieze relation holds at every solution of the Bethe equations | statement | theorem 6.8 | arxiv |
| The run-chain reduction | statement | proposition 6.10 | arxiv |
| Rationality of the Rogers sum | statement | corollary 6.6 | arxiv |
| The positive vacuum of every word: the propagated eigenvector | statement | theorem 6.4 | arxiv |
| The next-order Jacobian is a constant | statement | proposition F.3 | arxiv |
| The modular data of $\mathrm{TFT}_0$ | statement | theorem 19.5 | arxiv |
| The step identities | statement | lemma E.1 | arxiv |
| The sum rule for every word | statement | proposition 11.2 | arxiv |
| Reduction lemma | statement | lemma G.3 | arxiv |
| A0E3E3ZT85 | statement | corollary 13.2 | arxiv |
| Suslin normalisation | statement | proposition 13.5 | arxiv |
| C0RCFBDSJA | statement | proposition 2.1 | arxiv |
| Amphichirality | statement | proposition 5.2 | arxiv |
| The Rogers sums modulo $1$ | statement | proposition 13.8 | arxiv |
| Farey formula mod $24$ for $L^mR^m$ | statement | theorem 9.1 | arxiv |
| DGA6QPK1BS | statement | lemma 13.6 | arxiv |
| $L$-block lemma, $j=1$ | statement | lemma G.2 | arxiv |
| Positive solution of $L^mR^m$ | statement | theorem 6.3 | arxiv |
| Completeness for words with no singleton run | statement | theorem 12.3 | arxiv |
| Hill's formula at the two-run classes | statement | corollary 11.13 | arxiv |
| The index vector is the kernel vector of the monodromy | statement | fact 11.7 | arxiv |
| The flux-rule criterion at $\sigma V^*$ | statement | proposition 9.4 | arxiv |
| Crossings | statement | lemma 8.1 | arxiv |
| The trace is quantised, with modulus $\mathcal H/2^{\#L}$ | statement | fact 11.4 | arxiv |
| HMYN6A9T3F | statement | theorem 13.7 | arxiv |
| The $A_-$ sector of $L^mR^m$ at prime $m$ | statement | theorem 18.1 | arxiv |
| The parity of $E_{LL}$ | statement | lemma 13.3 | arxiv |
| The torsion formula | statement | theorem 10.1 | arxiv |
| Telescoping | statement | lemma F.1 | arxiv |
| The Wilson loop is a monomial in $1-x$ | statement | proposition 11.10 | arxiv |
| The linking form | statement | proposition 3.1 | arxiv |
| The Jacobian at the non-identity fixed points | statement | proposition 12.6 | arxiv |
| The metric group of the diagonal words is the untwisted one | statement | proposition 3.3 | arxiv |
| PRMBAZ2Y4A | statement | proposition 13.1 | arxiv |
| PZN86PRNJM | statement | proposition 13.4 | arxiv |
| The two systems are one | statement | proposition 6.1 | arxiv |
| Hill's formula at every class of every word | statement | theorem 11.12 | arxiv |
| The template splits into two refinements of one linking form | statement | fact 13.9 | arxiv |
| Farey formula mod $24$ for every hyperbolic word | statement | theorem 9.5 | arxiv |
| The recurrence of a frieze row | statement | lemma B.1 | arxiv |
| The diagonal words | statement | corollary 19.7 | arxiv |
| The corank of $\hat J_0$ | statement | theorem 17.1 | arxiv |
| The Bethe classes of every word | statement | theorem 11.6 | arxiv |
| The unit $A_+$ classes of a two-run word | statement | theorem 11.5 | arxiv |
| The fixed-point count | statement | theorem 12.1 | arxiv |
| The exact reduction | statement | proposition F.2 | arxiv |
| Interpretation | statement | corollary 12.8 | arxiv |
| The dominant saddle of the half-index is $V^*$ | statement | proposition 9.2 | arxiv |
| The $A_+$ sector constructs Evans--Gannon's $(H,\beta)$ | statement | fact 3.5 | arxiv |
| The $S$-matrix | statement | proposition 19.3 | arxiv |
| Finite-block lemma | statement | lemma G.4 | arxiv |
| WSV6RJEMQF | definition | definition | arxiv |
| The stretch factor at the positive vacuum | statement | proposition 6.5 | arxiv |
| The flux rule at the level of spins | statement | proposition 9.3 | arxiv |
| The pipeline produces the run-structure level matrix | statement | theorem 5.1 | arxiv |
| The effective central charge | statement | theorem 8.2 | arxiv |
| The $T$-matrix | statement | corollary 19.2 | arxiv |
| The Wilson line of charge $c$ is the row of the second identity object | statement | fact 19.8 | arxiv |
| The complete list of Gannon--Schopieray--Yadav | statement | fact 3.6 | arxiv |
| The template label | statement | corollary 13.10 | arxiv |
| ZVKMNCFZWY | statement | fact 11.3 | arxiv |
