Pith Number

pith:NTCDXNU4

pith:2014:NTCDXNU4F5CP53JWSHDMNTWVB6

not attested not anchored not stored refs pending

Infinite graphs that do not contain cycles of length four

Javier Cilleruelo

arxiv:1401.4502 v3 · 2014-01-18 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NTCDXNU4F5CP53JWSHDMNTWVB6}

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	2026-05-18T01:22:10.671812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cc43bb69c2f44feed3691c6c6ced50f8e839756abf07cbd06e03cfa4ef38e26

Aliases

arxiv: 1401.4502 · arxiv_version: 1401.4502v3 · doi: 10.48550/arxiv.1401.4502 · pith_short_12: NTCDXNU4F5CP · pith_short_16: NTCDXNU4F5CP53JW · pith_short_8: NTCDXNU4

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/NTCDXNU4F5CP53JWSHDMNTWVB6 \
  | 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: 6cc43bb69c2f44feed3691c6c6ced50f8e839756abf07cbd06e03cfa4ef38e26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28defb70ef2cf538363fc123a98eb867957e123e03706c4ccaa275dd33138443",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-01-18T01:03:31Z",
    "title_canon_sha256": "332852e759716d6fe2178d04d30c5478b888bd2dd56ea0ba8d04f8de4b61e3af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.4502",
    "kind": "arxiv",
    "version": 3
  }
}