# Active claim matrix

The six official active records below were extracted only for `Oj2I1xdKpv` from `claims.json` and `claims_anchored.json` at challenge revision `7b5b56aebf3abe590eab9f2c241a796125cab928`. The judge merges the anchored map after the default map, so its anchored entry replaces the default entry for this OpenReview ID. The two default records remain pinned in `evidence/claims.json` as source inputs, but are not active after this merge.

Evidence limit: every status below is **supported by a paper/source audit only**. This is not an independent reproduction, and it does not validate any author-reported number.

| Exact official claim | Source anchor | Evidence tier and status | Limit |
| --- | --- | --- | --- |
| On Newton Sketch, MCGS with the UCD criterion reaches 100% success using only 1,416 playouts, compared to 10,721 playouts for Preconditioned Weighted SGD and 25,158 for Block Randomized Kaczmarz (Table 2). | Paper Table 2 source and its search-efficiency table | Table audit: supported as reported | No result rerun. |
| MCGS reduces the number of playouts needed versus standard MCTS by roughly 2-3x by merging equivalent states in a DAG rather than a tree (Section 4.3, Table 2). | Paper Section 4.3 and Table 2 source | Table/source audit: supported as reported | No independent comparison. |
| The five-stage curriculum (Landweber iteration, Gradient Descent, Preconditioned GD, Sketched Preconditioned GD, Leverage-Score Subsampling) progressively increases problem difficulty, each stage introducing exactly one new failure mode resolved by one algorithmic component (Section 4.2, Table 1). | Paper Table 1 source and curriculum discussion | Table/source audit: supported as reported | No independent curriculum search. |
| Ablating the staged curriculum causes discovery of the Newton Sketch algorithm to fail completely (0% success across all partial curricula), while the full four-stage curriculum achieves 100% success (Table 7). | Paper Table 7 source | Table audit: supported as reported | No independent ablation. |
| MCGS sustains 50-58% state revisit rates during search, versus near-zero revisit rates for standard MCTS, demonstrating effective exploitation of shared subproblem structure (Figure 4). | Paper Figure 4/source discussion and scalability table | Source/table audit: supported as reported | No independent trace or rate calculation. |
| The discovered framework generalizes to eigenvalue problems (power iteration and sketched power iteration) with only one added normalization primitive, achieving 100% success on all three curriculum stages (Section 5.4, Table 3). | Paper Section 5.4 and Table 3 source | Table/source audit: supported as reported | No independent eigenvalue run. |

Direct sources: [OpenReview](https://openreview.net/forum?id=Oj2I1xdKpv), [arXiv](https://arxiv.org/abs/2605.18004), and [released repository](https://github.com/Tim-Xiong/RL4RLA).