| Ground-state energy benchmark | statement | lemma 2.9 | arxiv |
| Stabilizer nullity | definition | definition 4.12 | arxiv |
| Conditioning benchmark | definition | definition 1.1 | arxiv |
| MPS bond dimension | statement | corollary 1.6 | arxiv |
| Stability under discardable ancillas | statement | lemma 3.10 | arxiv |
| Large-$p$ product-stabilizer energy | statement | proposition 5.8 | arxiv |
| Sharp normalized stabilizer energy | statement | corollary 5.9 | arxiv |
| $k$-round magic classes | definition | definition 4.2 | arxiv |
| 4JANNYQ005 | definition | definition 3.1 | arxiv |
| Product-state energy benchmark | statement | lemma 2.8 | arxiv |
| Quadratic profile complexity | statement | corollary 2.7 | arxiv |
| Fixed-projection representation | statement | lemma 5.3 | arxiv |
| Profile entropy of forward magic | statement | lemma 4.8 | arxiv |
| 76X4ZHJD8V | statement | lemma 5.4 | arxiv |
| Conditioning and partial trace | statement | corollary 2.3 | arxiv |
| 7R6BP359RF | statement | lemma 4.13 | arxiv |
| Depth--width energy bounds | statement | proposition 3.6 | arxiv |
| Pauli-rotation normal form and nullity cost | statement | lemma B.5 | arxiv |
| Trace-norm comparison for the Pauli measurement | statement | lemma 2.1 | arxiv |
| Conditioning benchmark for Clifford+$T$ outputs | statement | corollary 5.2 | arxiv |
| Pauli action on the stabilizer eigenspace | statement | lemma B.2 | arxiv |
| Local realization of logical Pauli coordinates | statement | lemma B.3 | arxiv |
| Exact compression of discardable workspace | statement | lemma B.6 | arxiv |
| Product approximation after conditioning | statement | lemma 5.1 | arxiv |
| Stabilizer states reduce to product stabilizers | statement | corollary 5.6 | arxiv |
| Local-profile complexity principle | statement | theorem 1.2 | arxiv |
| Circuit size | statement | corollary 1.3 | arxiv |
| Reverse magic with arbitrary clean ancillas | statement | theorem 4.16 | arxiv |
| Profile entropy of $k$ magic rounds | statement | lemma 4.4 | arxiv |
| Energy of the exceptional factors | statement | lemma 5.5 | arxiv |
| Ancilla-independent logical core reduction | statement | proposition 4.14 | arxiv |
| Truncated squared conditioning with a prescribed POVM | statement | lemma 2.2 | arxiv |
| Clifford+$T$ circuits with discardable ancillas | statement | corollary 1.8 | arxiv |
| Nullity under Pauli rotations and conditioning | statement | lemma B.4 | arxiv |
| Entanglement depth | statement | corollary 1.5 | arxiv |
| HMBXCGVHJ1 | statement | lemma 3.3 | arxiv |
| Forward and reverse magic | definition | definition 4.1 | arxiv |
| Clean-ancilla reverse-magic entropy | statement | lemma 4.15 | arxiv |
| Canonical form of the conditioning approximation | statement | corollary 2.4 | arxiv |
| Backward-lightcone pruning for forward magic | statement | lemma 4.7 | arxiv |
| M4AX3PS3AW | statement | lemma A.1 | arxiv |
| Profile entropy of matrix product states | statement | lemma 3.13 | arxiv |
| Depth--width tradeoff | statement | corollary 1.4 | arxiv |
| Magic hierarchy | statement | corollary 1.7 | arxiv |
| Circuit-size energy bounds | statement | proposition 3.4 | arxiv |
| Block-product states | definition | definition 3.9 | arxiv |
| Every fixed number of magic rounds is separated from the ground state | statement | proposition 4.5 | arxiv |
| Q3E0VQMCN4 | statement | lemma 2.6 | arxiv |
| Block-product energy bounds | statement | proposition 3.12 | arxiv |
| Uniform cost of a conditioning budget | statement | lemma 2.5 | arxiv |
| Forward-magic energy bounds | statement | proposition 4.9 | arxiv |
| Mixed stabilizer states | definition | definition 4.6 | arxiv |
| Clean-ancilla reverse magic | definition | definition 4.11 | arxiv |
| Shallow circuit classes | definition | definition 3.5 | arxiv |
| Product-stabilizer thermodynamic limit | statement | lemma 5.7 | arxiv |
| Profile entropy of block-product states | statement | lemma 3.11 | arxiv |
| YJ1H26Y5SZ | statement | lemma 3.2 | arxiv |
| Stabilizer-nullity decomposition | statement | lemma B.1 | arxiv |
| Restriction growth of mixed stabilizer profiles | statement | lemma 4.10 | arxiv |
| Energy bounds for MPS | statement | proposition 3.14 | arxiv |
