Pith Number

pith:57K27UPR

pith:2013:57K27UPR6WIY7EHHVBKUGXD53L

not attested not anchored not stored refs pending

Computation of the Ramsey Numbers $R(C_4,K_9)$ and $R(C_4,K_{10})$

Alexander Lange, Ivan Livinsky, Stanis{\l}aw Radziszowski

arxiv:1310.3017 v1 · 2013-10-11 · 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{57K27UPR6WIY7EHHVBKUGXD53L}

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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	2026-05-18T03:10:45.241848Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efd5afd1f1f5918f90e7a855435c7ddad095f7b7d64d8cb0896c7af7ac85dcfa

Aliases

arxiv: 1310.3017 · arxiv_version: 1310.3017v1 · doi: 10.48550/arxiv.1310.3017 · pith_short_12: 57K27UPR6WIY · pith_short_16: 57K27UPR6WIY7EHH · pith_short_8: 57K27UPR

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/57K27UPR6WIY7EHHVBKUGXD53L \
  | 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: efd5afd1f1f5918f90e7a855435c7ddad095f7b7d64d8cb0896c7af7ac85dcfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0c9e1ec6e29466e871c1b490845d4e883cfee2e3609eed62701751c071072ea",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-10-11T04:16:29Z",
    "title_canon_sha256": "a6eb23f40212150dddfdb977bea734f28dcb487252adf656aed01cc8d258b545"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.3017",
    "kind": "arxiv",
    "version": 1
  }
}