Pith Number

pith:U6GID774

pith:2013:U6GID774GXN4TCI37OPPSPIV7T

not attested not anchored not stored refs pending

Empty triangles in good drawings of the complete graph

Alexander Pilz, Birgit Vogtenhuber, Oswin Aichholzer, Pedro A. Ramos, Thomas Hackl, Vera Sacrist\'an

arxiv:1306.5081 v1 · 2013-06-21 · cs.CG · cs.DM · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U6GID774GXN4TCI37OPPSPIV7T}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:20:19.788939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a78c81fffc35dbc9891bfb9ef93d15fce7a15189bc5d3a9d2597504436f5af29

Aliases

arxiv: 1306.5081 · arxiv_version: 1306.5081v1 · doi: 10.48550/arxiv.1306.5081 · pith_short_12: U6GID774GXN4 · pith_short_16: U6GID774GXN4TCI3 · pith_short_8: U6GID774

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U6GID774GXN4TCI37OPPSPIV7T \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a78c81fffc35dbc9891bfb9ef93d15fce7a15189bc5d3a9d2597504436f5af29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7288c14e16d960b97f6cdd19c5976ac11ac4ff59a83479eb094a7d03442280f",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2013-06-21T09:28:16Z",
    "title_canon_sha256": "c26d5cc0da504d3ae0cef85cf0967373b29801c5908309f8e3dda0a3a11c3113"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.5081",
    "kind": "arxiv",
    "version": 1
  }
}