Explore first
Primary entry points are curated candidates and lookup — not a single sync search button.
Hall of Fame
Persistent board of geometries that passed dataset target rules, each with a shareable dossier page.
Lookup
Identify a Hodge triple and open its dossier without waiting on a live ranking job.
Quintic candidate
Open the classic mirror-quintic-style example dossier (synthetic / literature Hodge pair).
Optional: run a live ranking
Secondary demo: rank ~5,000 synthetic draws. Metrics are synthetic retrieval vs random baseline — target-defining features are held out of the model. Runtime is typically a few seconds.
For Scientists
Use upg-strings as a reproducible filter before deeper analysis — with clear limits on what “verified” means.
- Rank synthetic candidates by likelihood of meeting a dataset target rule
- Check top-k hits against that rule (synthetic labels) for retrieval-style precision/recall
- Export CSV/JSON artifacts; open shareable dossiers from Hall of Fame
- Repeat with fixed seeds for reproducible comparisons
Outputs
results_topk.csv
Top-ranked candidates with scores and target-rule status
metrics.json
Synthetic retrieval metrics, baseline, and honesty / leakage notes
repro.md
Complete reproducibility report with environment details
Compatible exports: CYTools, cymetric, Sage, Mathematica, plus JSON/CSV.
Metrics (honest framing)
Precision@k
Fraction of top-k that pass the synthetic target rule — vs random baseline in the same draw
Recall@k
Fraction of all rule-positive rows found in top-k
Hold-out
Target-defining columns (e.g. |χ|) are withheld from the RandomForest
Links
Disclaimer: Demo corpora are synthetic Hodge draws. This tool ranks and packages candidate dossiers for exploration — Verified means a dataset target-rule match on those labels.