Pith Number

pith:Y5QUX4EX

pith:2011:Y5QUX4EXMK2H5VFZEPBG433JMD

not attested not anchored not stored refs pending

An f-chromatic spanning forest of edge-colored complete bipartite graphs

Kazuhiro Suzuki

arxiv:1106.2441 v1 · 2011-06-13 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y5QUX4EXMK2H5VFZEPBG433JMD}

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	2026-05-18T00:08:31.843704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7614bf09762b47ed4b923c26e6f6960dcb6063be6bd23c63c3d7b3472b5039d

Aliases

arxiv: 1106.2441 · arxiv_version: 1106.2441v1 · doi: 10.48550/arxiv.1106.2441 · pith_short_12: Y5QUX4EXMK2H · pith_short_16: Y5QUX4EXMK2H5VFZ · pith_short_8: Y5QUX4EX

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/Y5QUX4EXMK2H5VFZEPBG433JMD \
  | 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: c7614bf09762b47ed4b923c26e6f6960dcb6063be6bd23c63c3d7b3472b5039d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d346f39857d4e5aff6f9a1d0b07237b20dd77f6256fcbe3e5e81b8b908cb4928",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-06-13T13:40:06Z",
    "title_canon_sha256": "07a43104e94125dc8e62b3bdb116c2ad214077d85f7dec576976d04a1543261f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2441",
    "kind": "arxiv",
    "version": 1
  }
}