Pith Number

pith:IG2NU566

pith:2022:IG2NU566E7MYDNHL52YVXKIDIL

not attested not anchored not stored refs pending

Expected number of faces in a random embedding of any graph is at most linear

Bojan Mohar, Jesse Campion Loth

arxiv:2202.07746 v2 · 2022-02-15 · 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{IG2NU566E7MYDNHL52YVXKIDIL}

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	2026-07-05T05:56:37.876480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41b4da77de27d981b4ebeeb15ba90342d57634db90fd47cc5efaa38f425904a7

Aliases

arxiv: 2202.07746 · arxiv_version: 2202.07746v2 · doi: 10.48550/arxiv.2202.07746 · pith_short_12: IG2NU566E7MY · pith_short_16: IG2NU566E7MYDNHL · pith_short_8: IG2NU566

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/IG2NU566E7MYDNHL52YVXKIDIL \
  | 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: 41b4da77de27d981b4ebeeb15ba90342d57634db90fd47cc5efaa38f425904a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dfd9bab9d78ada88911b7b4b217d99666a560e50042b6145c703c2a0aa2b45d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-02-15T21:57:10Z",
    "title_canon_sha256": "cd3dbfbf5bc33b0298c204181e538b6250078c1f4db387caa3b528b877e59e45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2202.07746",
    "kind": "arxiv",
    "version": 2
  }
}