Pith Number

pith:NEECP6LT

pith:2022:NEECP6LTOLCXUGZRVUSGA5YDCZ

not attested not anchored not stored refs pending

The odd chromatic number of a planar graph is at most 8

Jan Petr, Julien Portier

arxiv:2201.12381 v2 · 2022-01-28 · 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{NEECP6LTOLCXUGZRVUSGA5YDCZ}

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	2026-07-05T05:52:07.122246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

690827f97372c57a1b31ad2460770316507799d84b2a06b40a7b7e658f0ee004

Aliases

arxiv: 2201.12381 · arxiv_version: 2201.12381v2 · doi: 10.48550/arxiv.2201.12381 · pith_short_12: NEECP6LTOLCX · pith_short_16: NEECP6LTOLCXUGZR · pith_short_8: NEECP6LT

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/NEECP6LTOLCXUGZRVUSGA5YDCZ \
  | 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: 690827f97372c57a1b31ad2460770316507799d84b2a06b40a7b7e658f0ee004

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05d2fb27ce19a87c77c4d53cbf47d69225e372bfb8f71d86650dedb417f5ef1d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-01-28T19:22:20Z",
    "title_canon_sha256": "b330a12976e83af60caa67cbf2fea8de670f1bc1a0ddd5026402a12c56b348de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.12381",
    "kind": "arxiv",
    "version": 2
  }
}