# Kael Research

> Kael Research independently rebuilds and tests claims in new research papers. Five cases are published as of 3 October 2026, each with methods, measured data, source credit and limitations.

## Published cases

- [Case 001: Does two-choice linear probing hold up?](https://kaelresearch.com/papers/2610.00688): At 99% load, greedy two-choice averaged 5.797400 successful-lookup probes versus 51.024915 for the ordered one-choice control across five seeds. CPU timings are preliminary; the separate 2.1590-probe full-table offline result awaits a second review.

- [Case 002: Does the 52-addition 3×3 matrix scheme work?](https://kaelresearch.com/papers/2609.06588): Yes: all 729 ordered coefficients match, and the scheme works over noncommutative rings. Direct Python is slower than NumPy; historical search claims remain untested.
- [Case 003: Are new shortest-path algorithms faster than Dijkstra?](https://kaelresearch.com/papers/shortest-paths): Not on four US road maps in our implementations: 1,600 certified quiet-server road runs, with median slowdowns about 6–75×. These timings do not test the papers' asymptotic bounds.
- [Case 004: Does SAMuon beat Muon? A small-scale test](https://kaelresearch.com/papers/2608.25990): At 0.056M–0.788M parameters SAMuon had lower median final loss at each size; post-hoc tokens-to-target were mixed, and the spectral stability mechanism did not reproduce.
- [Case 005: Does tokenizer search matter more than its objective?](https://kaelresearch.com/papers/2609.19145): The published intrinsic measurements mostly reproduce (92/96 Table 1 values), but a tiny 1.32M-parameter test did not show the bottom-up BPB advantage. Paper-scale behavior remains open.

## Explore

- [All cases](https://kaelresearch.com/cases): Five published paper tests with evidence and raw data.
- [How we test a paper](https://kaelresearch.com/method): Correctness, calibration, fair baselines, repeated runs, raw data and review precede verdicts.
- [Corrections log](https://kaelresearch.com/corrections): Case 001's initial paper-bug allegation was withdrawn after review found an agent had misread a lookup rule.
- [Full case text for AI readers](https://kaelresearch.com/llms-full.txt): A Markdown account of the published findings and limitations.