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OPEN COMPUTATIONAL GEOMETRY · V1 RELEASE CANDIDATE

A living map of
what fits.

Verified constructions, best-known records, and unsolved regions—mapped across triangle shape and container geometry.

— verified records 04 family slices — open problems
Explore the phase map ↓

THE SIGNATURE VIEW

Where patterns change.

Move through shape space. Each cell names the dominant observed construction and its evidence level—not a universal claim of optimality.

TRIANGLE APEX →
RECTANGLE ASPECT RATIO → · loading computed release…
LIVE SLICE60° / 1.50:1
triangle areaboundary waste

FAMILY EXPLORER

Three starting territories.

01

Right

Exact rectangular pairings supply the Atlas’s known-optimum controls.

PROVEN CONTROLS
02

Equilateral

Periodic interiors expose the finite boundary-loss problem most clearly.

VERIFIED SLICES
03

Isosceles

Right-isosceles controls anchor a much larger, mostly open shape family.

CONTROL + OPEN

VERIFIED RECORDS

Inspect the evidence.

Curated release ↓304-record research release ↓

PATTERN COMPARISON

Same question, different structure.

Compare records by verified utilization, optimality gap, and where unused area accumulates.

versus

OPEN-PROBLEM BROWSER

The blank parts are the point.

Every open region is an invitation: reproduce a baseline, improve a record, or tighten a bound.

RECORD LEADERBOARD

Strong results, traceable people.

Rankings use independently verified density. Reproducibility and attribution travel with every coordinate set.

COMMUNITY PIPELINE

Bring coordinates,
not screenshots.

  1. 01 Submit JSON
  2. 02 Verify geometry
  3. 03 Compare record
  4. 04 Review evidence
  5. 05 Publish

Submissions are checked for schema validity, overlaps, boundary violations, duplicate fingerprints, and whether they improve the current record. Proofs and citations always require human review.

Contribute on GitHub ↗

RESEARCH EXPANSION · MILESTONE 9

From atlas to open endeavor.

NOW

Finite rectangles

Right, equilateral, and isosceles slices with reproducible records.

NEXT

Scalene space

Normalized two-angle phase maps and verified solver baselines.

THEN

Bounds & literature

Rigorous upper bounds, citation ingestion, and finite/asymptotic comparison.

OPEN

Distributed studies

Versioned challenge sets for classrooms, researchers, and solver fleets.

LITERATURE REGISTRY

Related work, scoped precisely.

Primary sources are classified by their exact relationship to the Atlas. Context and methods never become numerical claims by implication.

V1 GATE · 1.0.0-RC.1

Verified in two languages.
Honest about what remains.

The v1 candidate includes 304 records, independent JavaScript and Python verification, solver tournaments, proof certificates, literature scope, community acceptance tests, and complete archival metadata.

Release status
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Download v1 candidate dataset ↓