Pith Number

pith:FJI5RJM6

pith:2023:FJI5RJM6UQEL5AXUUNWMV3RQGE

not attested not anchored not stored refs pending

Solution to a problem of Gr\"unbaum on the edge density of $4$-critical planar graphs

Carl Feghali, Zden\v{e}k Dvo\v{r}\'ak

arxiv:2311.03132 v1 · 2023-11-06 · 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{FJI5RJM6UQEL5AXUUNWMV3RQGE}

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	2026-07-05T07:09:36.619189Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a51d8a59ea408be82f4a36ccaee303120c2944d0fbeb3d20c261a4026fb38cc

Aliases

arxiv: 2311.03132 · arxiv_version: 2311.03132v1 · doi: 10.48550/arxiv.2311.03132 · pith_short_12: FJI5RJM6UQEL · pith_short_16: FJI5RJM6UQEL5AXU · pith_short_8: FJI5RJM6

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/FJI5RJM6UQEL5AXUUNWMV3RQGE \
  | 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: 2a51d8a59ea408be82f4a36ccaee303120c2944d0fbeb3d20c261a4026fb38cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b52eee30c6bb48efcca3a71c5034df21b3c1ad2db819a8be5458a10f5e5fc781",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-11-06T14:28:33Z",
    "title_canon_sha256": "82bc20e14dfcb25f00910307495c64e7cb945a07825d565077bb3224a082dc43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.03132",
    "kind": "arxiv",
    "version": 1
  }
}