| Strong correlation breaker with advice | definition | definition 2.14 | arxiv |
| Expected Queries and Query Tails | statement | proposition 5.11 | arxiv |
| Prescribed output length and error | statement | proposition 5.8 | arxiv |
| Correlation breaker with advice | statement | theorem 2.15 | arxiv |
| Tagged matching bound | statement | theorem 6.13 | arxiv |
| A linear seeded extractor with a tunable seed length | statement | theorem 2.13 | arxiv |
| Common constant spaces | statement | lemma 5.3 | arxiv |
| Affine non-malleability implies average-case hardness | statement | theorem 1.6 | arxiv |
| Assembly | statement | lemma B.11 | arxiv |
| Fourier correlations between the two outputs | statement | lemma 3.11 | arxiv |
| Decorrelation across disjoint affine sections | definition | definition 4.3 | arxiv |
| Tagged lifting | statement | corollary 6.14 | arxiv |
| Partial condensation | statement | lemma 6.23 | arxiv |
| Constant row weight | statement | lemma 6.25 | arxiv |
| Logarithmic overhead from sumset extractors | statement | theorem 5.25 | arxiv |
| Conditioning on the displacement | statement | lemma 4.5 | arxiv |
| Prescribed joint output patterns | statement | lemma 6.16 | arxiv |
| Non-Oblivious Local Depth | statement | theorem 1.10 | arxiv |
| Direct overlapping size--depth tradeoff | statement | theorem 1.11 | arxiv |
| Non-malleable affine extractors for sublinear entropy | statement | theorem 1.3 | arxiv |
| Explicit bounded-depth lower bounds | statement | corollary 6.11 | arxiv |
| Selecting a good block | statement | lemma 3.10 | arxiv |
| Non-malleable affine extractor | definition | definition 1.1 | arxiv |
| An Affine Space Through a Prescribed Common Zero | statement | lemma 5.16 | arxiv |
| Rank certificate | definition | definition B.1 | arxiv |
| Independence merging | statement | lemma 2.3 | arxiv |
| List Prediction with Independent Uniform Auxiliary Inputs | statement | theorem A.6 | arxiv |
| Tseitin legal assignments | statement | lemma 6.10 | arxiv |
| 8WBT40CMN5 | statement | corollary 6.22 | arxiv |
| Universal rank certificate | statement | theorem B.6 | arxiv |
| Average-case bounds | statement | proposition 5.2 | arxiv |
| Directional derivative bias | definition | definition 4.2 | arxiv |
| Affine conditioning | statement | lemma 2.6 | arxiv |
| Non-malleable affine extractors | statement | corollary 5.29 | arxiv |
| Generic exact bounds | statement | theorem 5.4 | arxiv |
| Ingredients for the initial seed | statement | lemma 3.6 | arxiv |
| Depth From Affine Dispersion | statement | theorem 5.17 | arxiv |
| Disjoint majority restrictions | statement | lemma 6.18 | arxiv |
| An asymmetric separated partition | statement | lemma 5.26 | arxiv |
| Advice generator | statement | lemma 3.4 | arxiv |
| The affine-state invariant | statement | lemma 6.7 | arxiv |
| Non-malleability under translations and low-degree correlation | statement | theorem 5.12 | arxiv |
| Ordered accumulator | statement | lemma 6.27 | arxiv |
| List prediction | statement | theorem A.5 | arxiv |
| Affine non-malleability implies weakly read-once hardness | statement | theorem 4.11 | arxiv |
| Correlation with quadratic polynomials | statement | lemma 5.1 | arxiv |
| Lower bound on clause rank | statement | corollary 6.8 | arxiv |
| A cut of bounded size in a full program | statement | lemma 4.6 | arxiv |
| Non-oblivious degree-$2$ depth upper bound | statement | proposition 5.7 | arxiv |
| Growing Query Degree | statement | corollary 5.15 | arxiv |
| D1MT156V4C | statement | lemma B.15 | arxiv |
| Simultaneous selection | statement | lemma B.10 | arxiv |
| Bounded-degree affine extractors | statement | theorem 2.16 | arxiv |
| Weakly read-once linear branching program | definition | definition 4.1 | arxiv |
| DWRE6J6KSV | statement | theorem 3.13 | arxiv |
| Separated leaves | statement | proposition 5.23 | arxiv |
| Directional hardness with independent uniform auxiliary variables | statement | theorem A.2 | arxiv |
| Normalization and coordinate enlargement | statement | lemma B.7 | arxiv |
| A cut for the pure-input rank | statement | lemma A.1 | arxiv |
| ERF9RSGMQQ | statement | lemma B.14 | arxiv |
| Alignment to original family blocks | statement | lemma B.9 | arxiv |
| Overlapping size--depth transfer | statement | theorem 6.19 | arxiv |
| Fixed Multiple Tamperings | statement | proposition 5.9 | arxiv |
| Higher moments with independent uniform auxiliary variables | statement | theorem A.9 | arxiv |
| Grouped matrix | statement | lemma 6.24 | arxiv |
| Deterministic Lossless Lifting | statement | theorem 6.1 | arxiv |
| Affine hardness with independent uniform auxiliary variables | statement | theorem A.4 | arxiv |
| Conditioning affine sources | statement | lemma 2.5 | arxiv |
| Non-malleable affine extractors for jointly affine inputs | statement | theorem 3.14 | arxiv |
| Boolean projection rounding | statement | lemma B.4 | arxiv |
| Monotone closure | statement | lemma 6.6 | arxiv |
| Affine sections from future transcripts | statement | lemma 4.7 | arxiv |
| Intersecting projected sections | statement | lemma A.3 | arxiv |
| Combining the outputs | statement | theorem 3.9 | arxiv |
| Repair with an additive defect bound | statement | lemma B.8 | arxiv |
| HDH1C3JBHY | statement | theorem 3.17 | arxiv |
| Affine fibers and sections | definition | definition 2.4 | arxiv |
| Directional derivative bounds on separated leaves | statement | lemma 5.27 | arxiv |
| Lower bounds on extractor error | statement | lemma 5.5 | arxiv |
| HWW8Q37F2D | statement | corollary 3.12 | arxiv |
| Deterministic Simultaneous Surjectivity | statement | theorem 6.2 | arxiv |
| A restricted gadget | statement | lemma 6.3 | arxiv |
| Local hardness from directional derivative bounds | statement | theorem 5.28 | arxiv |
| Output probabilities on safe affine spaces | statement | lemma 6.5 | arxiv |
| Linear seeded extractors | statement | theorem 2.12 | arxiv |
| $t$-Non-Malleable Affine Extractor | definition | definition 2.10 | arxiv |
| KHR8C3QAS8 | statement | lemma 2.1 | arxiv |
| Non-Oblivious Depth at Fixed Entropy Rate | statement | theorem 1.9 | arxiv |
| Higher moments for list prediction | statement | theorem A.8 | arxiv |
| Strong seeded extractor | definition | definition 2.2 | arxiv |
| Quadratic size--depth tradeoff | statement | theorem 1.12 | arxiv |
| Signed completion to the entropy threshold | statement | lemma 5.22 | arxiv |
| Higher moments | statement | theorem A.7 | arxiv |
| N5833TA5VD | statement | lemma B.13 | arxiv |
| Correlation Transfer | statement | proposition 5.10 | arxiv |
| Moments with a linear character | statement | lemma 6.4 | arxiv |
| NTN9FZ3S43 | statement | corollary 3.19 | arxiv |
| P7QQW5BK2V | statement | lemma B.12 | arxiv |
| Equivalent Jointly Affine Formulation | statement | lemma 2.11 | arxiv |
| Directional affine extractor | definition | definition 1.4 | arxiv |
| Affine non-malleability implies section decorrelation | statement | lemma 4.4 | arxiv |
| Properties of one iteration | statement | proposition 3.7 | arxiv |
| PQVQJSGHF0 | statement | corollary 5.20 | arxiv |
| Q4EQ6B2D0J | statement | theorem 6.21 | arxiv |
| Directional affine extractors imply weakly read-once hardness | statement | theorem 4.10 | arxiv |
| Growing an Affine Row | statement | lemma 3.5 | arxiv |
| Matching Bounds at Fixed Entropy Rate | statement | corollary 5.13 | arxiv |
| Counting displacements | statement | lemma A.10 | arxiv |
| Non-oblivious and oblivious degree-$2$ decision-tree depth | statement | theorem 1.8 | arxiv |
| A fixed number of affine tamperings | statement | corollary 3.15 | arxiv |
| Correlation bound | statement | theorem 4.8 | arxiv |
| Separating the path supports | statement | lemma 5.24 | arxiv |
| Common bad-seed set | statement | lemma 2.9 | arxiv |
| Legal partial assignments | definition | definition 2.17 | arxiv |
| Conditioning on several outputs | statement | lemma 3.16 | arxiv |
| Block length | statement | lemma 6.17 | arxiv |
| V194YME2QM | statement | lemma 2.8 | arxiv |
| Exponential average-case hardness | statement | corollary 1.7 | arxiv |
| Exact uniformity on affine fibers | statement | corollary 3.2 | arxiv |
| Partitioning according to equalities among tampered inputs | statement | lemma 3.18 | arxiv |
| Cluster product bound | statement | theorem B.2 | arxiv |
| Directional overlapping-gadget lifting | statement | theorem 6.9 | arxiv |
| Sublinear Entropy at Fixed Degree | statement | corollary 5.14 | arxiv |
| Directional affine extractors imply average-case hardness | statement | theorem 1.5 | arxiv |
| Rectangular block completion | statement | lemma B.5 | arxiv |
| Correlation with bounded-degree polynomial phases | statement | lemma 3.8 | arxiv |
| Rectangle depth bound | statement | theorem 5.18 | arxiv |
| Prescribed Output and Error | statement | corollary 3.20 | arxiv |
| WK90YNQB5C | statement | lemma 6.26 | arxiv |
| Small localities | statement | proposition 5.19 | arxiv |
| XQGQ53YRVX | statement | corollary 6.20 | arxiv |
| Cubic trace on affine sections | statement | lemma A.11 | arxiv |
| YVSW5PB8QC | statement | theorem B.16 | arxiv |
| The cubic trace function | statement | corollary 4.12 | arxiv |
| Non-malleable affine extractors for linear entropy | statement | theorem 1.2 | arxiv |
| Rank capacities for two conditioning spaces | statement | lemma B.3 | arxiv |
| Correlation breaking with intermediate variables | statement | lemma 3.1 | arxiv |
| A parameter consequence | statement | corollary 5.30 | arxiv |
