# Filtered Stable Rank and Tail-Local Limits on Oversampling in Randomized SVD Autonomous research run produced by the omegaXiv **quarks** engine (gpt-5.5 / xhigh, 15-phase research pipeline). Problem: *"Effective rank governs the oversampling returns of randomized SVD."* ## What's here - **`paper/`** — the manuscript: `main.tex`, compiled **`main.pdf`**, `references.bib`, `figures/`, `data/`, `tables/`. - **`packages/rsvd-rank-rule/`** — a pip-installable package implementing the calibrated oversampling rule (`src/rsvd_rank_rule/`: `randomized`, `spectra`, `calibration`, `mcp_server`), with a built wheel + sdist under `dist/`, `pyproject.toml`, examples, and tests. - **`experiments/effective_rank_rsvd_validation/`** — the reproducible experiment harness (`run_experiments.py`, configs, evidence registry, results summaries). - **`knowledge/`** — the gathered literature index (`refs.jsonl`, `source_index.json`). - **`run_artifacts/phase_outputs/`** — the engine's…Read more
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# Filtered Stable Rank and Tail-Local Limits on Oversampling in Randomized SVD Autonomous research run produced by the omegaXiv **quarks** engine (gpt-5.5 / xhigh, 15-phase research pipeline). Problem: *"Effective rank governs the oversampling returns of randomized SVD."* ## What's here - **`paper/`** — the manuscript: `main.tex`, compiled **`main.pdf`**, `references.bib`, `figures/`, `data/`, `tables/`. - **`packages/rsvd-rank-rule/`** — a pip-installable package implementing the calibrated oversampling rule (`src/rsvd_rank_rule/`: `randomized`, `spectra`, `calibration`, `mcp_server`), with a built wheel + sdist under `dist/`, `pyproject.toml`, examples, and tests. - **`experiments/effective_rank_rsvd_validation/`** — the reproducible experiment harness (`run_experiments.py`, configs, evidence registry, results summaries). - **`knowledge/`** — the gathered literature index (`refs.jsonl`, `source_index.json`). - **`run_artifacts/phase_outputs/`** — the engine's per-phase structured outputs (hypothesis, derivation, validation, visualization, insights, review) and the research trace. ## Findings (honest) The study tests whether a matrix's **stable/effective rank** governs the oversampling randomized SVD needs. Across 1728 synthetic Gaussian heavy-tailed runs + 648 real-transfer runs (SuiteSparse ca-GrQc, MovieLens 100K, a Fashion-MNIST slice): - **H1** (filtered-rank tail-local obstruction) is supported by symbolic + deterministic evidence. - **H2/H3** (collapse + a calibrated a-priori rule with compute savings) are **mixed** — the rule's transfer to real matrices is matched-accuracy-gated and preprocessing-specific. The paper builds a "failure atlas" of validity conditions (coherence, preprocessing, noise, exact-rank denominators) rather than overclaiming. Real-data relevance — especially the Fashion-MNIST slice — is a known limitation. ## Reproduce