Pith Number

pith:5UQCP2VU

pith:2012:5UQCP2VUKEIFMG5FNFBBRLBV34

not attested not anchored not stored refs pending

A New Lower Bound for the Ramsey Number R(4, 8)

Hiroshi Fujita

arxiv:1212.1328 v3 · 2012-12-06 · cs.DM · 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{5UQCP2VUKEIFMG5FNFBBRLBV34}

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	2026-05-18T03:29:26.930656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed2027eab45110561ba5694218ac35df054c05021a09a7fcf346f02c38322a7c

Aliases

arxiv: 1212.1328 · arxiv_version: 1212.1328v3 · doi: 10.48550/arxiv.1212.1328 · pith_short_12: 5UQCP2VUKEIF · pith_short_16: 5UQCP2VUKEIFMG5F · pith_short_8: 5UQCP2VU

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/5UQCP2VUKEIFMG5FNFBBRLBV34 \
  | 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: ed2027eab45110561ba5694218ac35df054c05021a09a7fcf346f02c38322a7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c7c36dbe74a6f9c2562f52c0305cf69bfaa36147109cf306ad797d702272d08",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-12-06T14:04:42Z",
    "title_canon_sha256": "a29ea7d41d8435302dfbb5cc57ad0faf9238e570b6bb3227917bfaa04cdbc846"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1328",
    "kind": "arxiv",
    "version": 3
  }
}