Pith Number

pith:4BAPB5YW

pith:2020:4BAPB5YWUTDWYOPSREQU5F2NS5

not attested not anchored not stored refs pending

The mod $k$ chromatic index of graphs is $O(k)$

F\'abio Botler, Lucas Colucci, Yoshiharu Kohayakawa

arxiv:2007.08324 v1 · 2020-07-16 · 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{4BAPB5YWUTDWYOPSREQU5F2NS5}

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	2026-07-05T01:19:45.926839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e040f0f716a4c76c39f289214e974d975bc9cba5ba91c90184831d52abe108cc

Aliases

arxiv: 2007.08324 · arxiv_version: 2007.08324v1 · doi: 10.48550/arxiv.2007.08324 · pith_short_12: 4BAPB5YWUTDW · pith_short_16: 4BAPB5YWUTDWYOPS · pith_short_8: 4BAPB5YW

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/4BAPB5YWUTDWYOPSREQU5F2NS5 \
  | 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: e040f0f716a4c76c39f289214e974d975bc9cba5ba91c90184831d52abe108cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e59a9dbd0bac978bbc4566d1a27a1b11b2c6f72192b6a76dc46cd6a04a9852ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-07-16T13:31:54Z",
    "title_canon_sha256": "197b0ed8cf275614d3ec373e452df914410612358bcb27793ab8a3a96ac519a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.08324",
    "kind": "arxiv",
    "version": 1
  }
}