| Null Law | definition | definition 6.8 | arxiv |
| Commutants of $O(N,\Z)$ | statement | lemma 3.3 | arxiv |
| Recovery of the Average Discrete Gradient | statement | theorem 5.5 | arxiv |
| Persistent Strong Recovery above the Algorithmic Threshold for Every Tensor Order | statement | theorem 7.1 | arxiv |
| Concentration of Dynkin martingales | statement | lemma 3.10 | arxiv |
| Gauge-Transformed Hamiltonian | statement | lemma 6.6 | arxiv |
| Informal | statement | theorem 1.2 | arxiv |
| 5A1J5TM83X | statement | lemma 6.15 | arxiv |
| Discrete Sobolev Norm | definition | definition 3.5 | arxiv |
| Recovery of the Average Discrete Hessian | statement | theorem 5.7 | arxiv |
| Adaptive Contiguity Estimate | statement | theorem 6.10 | arxiv |
| Correlation of the Sign-Rounded Average Discrete Gradient | statement | corollary 4.3 | arxiv |
| Persistent Strong Recovery above the Algorithmic Threshold | statement | theorem 6.1 | arxiv |
| Persistent Strong Recovery after Weak Recovery | statement | theorem 7.4 | arxiv |
| Bakry--\'Emery Type Discrete Gradient Estimate for the Hypercube | statement | lemma 5.2 | arxiv |
| Signal-Noise Decomposition of the Average Discrete Gradient | statement | theorem 4.1 | arxiv |
| Uniform Concentration along the Null Trajectory | statement | lemma 6.9 | arxiv |
| Persistent Strong Recovery Slightly above the Algorithmic Threshold | statement | corollary 6.3 | arxiv |
| Sobolev norm bounds for the signal term | statement | lemma 3.7 | arxiv |
| Planted Law | definition | definition 6.7 | arxiv |
| Dynkin's Formula for Continuous-time Glauber dynamics | statement | lemma 3.9 | arxiv |
| Stein's Lemma for the hypercube | statement | lemma 3.2 | arxiv |
| KN7W99TVVR | statement | lemma 4.4 | arxiv |
| Regularity of the Null Hamiltonian | statement | lemma 6.13 | arxiv |
| Concentration of matrix-valued Dynkin martingales | statement | lemma 3.11 | arxiv |
| Correlation of the Warm Start | statement | lemma 6.12 | arxiv |
| Discrete product rule | statement | lemma 3.1 | arxiv |
| Critical Recovery from a Sufficiently Warm Start | statement | theorem 6.4 | arxiv |
| Decomposition of the $k$-Spin Hamiltonian | statement | lemma 6.5 | arxiv |
| Change of Measure for Single-Site Dynamics | statement | lemma 3.13 | arxiv |
| Persistent Strong Recovery after Critical Correlation | statement | theorem 6.2 | arxiv |
| Moments of Rademacher sums | statement | lemma 3.4 | arxiv |
| Properties of the Green operator | statement | lemma 5.3 | arxiv |
| Properties of the Hessian observable | statement | lemma 5.6 | arxiv |
| Sobolev norm concentration for the Ising pure $k$-spin Hamiltonian | statement | lemma 3.6 | arxiv |
| Recovery by Ergodic Averaging for Tensor PCA | statement | theorem 5.1 | arxiv |
| Informal | statement | theorem 1.1 | arxiv |
| Recovery by the Augmented Ergodic Second Moment for Tensor PCA | statement | theorem 7.2 | arxiv |
| Bounds on the Signal Drift | statement | lemma 6.14 | arxiv |
| Signal-Noise Decomposition of the Average Discrete Hessian | statement | theorem 4.5 | arxiv |
