Pith Number

pith:OQSGKZMZ

pith:2015:OQSGKZMZB227BOJ7GTDIY3IYBX

not attested not anchored not stored refs pending

Tight Lower and Upper Bounds for the Complexity of Canonical Colour Refinement

Christoph Berkholz, Martin Grohe, Paul Bonsma

arxiv:1509.08251 v1 · 2015-09-28 · cs.DS · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OQSGKZMZB227BOJ7GTDIY3IYBX}

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	2026-05-18T01:31:54.309850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74246565990eb5f0b93f34c68c6d180dfff99cca4f8fea8b20722a6bf59d93ee

Aliases

arxiv: 1509.08251 · arxiv_version: 1509.08251v1 · doi: 10.48550/arxiv.1509.08251 · pith_short_12: OQSGKZMZB227 · pith_short_16: OQSGKZMZB227BOJ7 · pith_short_8: OQSGKZMZ

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/OQSGKZMZB227BOJ7GTDIY3IYBX \
  | 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: 74246565990eb5f0b93f34c68c6d180dfff99cca4f8fea8b20722a6bf59d93ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a3ef8ec108f42f838cc3128e58401b1502bec38563952685271deffa002e3e9",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2015-09-28T09:36:08Z",
    "title_canon_sha256": "9fedd9de13e90ab5b82b92f6ec4093d25eadd676418a892e4e4d1bd8e8255a9c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08251",
    "kind": "arxiv",
    "version": 1
  }
}