Pith Number

pith:MSG3SFJJ

pith:2007:MSG3SFJJ4XXD5SNUHNSXRMLO72

not attested not anchored not stored refs pending

Constrained Ramsey Numbers

Benny Sudakov, Po-Shen Loh

arxiv:0706.2107 v2 · 2007-06-14 · 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{MSG3SFJJ4XXD5SNUHNSXRMLO72}

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	2026-05-18T04:09:16.202384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

648db91529e5ee3ec9b43b6578b16efea2005b4788cb6d9ef9f29bb595a5fae2

Aliases

arxiv: 0706.2107 · arxiv_version: 0706.2107v2 · doi: 10.48550/arxiv.0706.2107 · pith_short_12: MSG3SFJJ4XXD · pith_short_16: MSG3SFJJ4XXD5SNU · pith_short_8: MSG3SFJJ

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/MSG3SFJJ4XXD5SNUHNSXRMLO72 \
  | 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: 648db91529e5ee3ec9b43b6578b16efea2005b4788cb6d9ef9f29bb595a5fae2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "501d9199e7cd04681791f0f84bf27d23612ab5e484b6abdf171277136696dcd0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-06-14T12:25:48Z",
    "title_canon_sha256": "cc62298a8dbeb4ee9d1faa59bc87d38db5af0ef33821a32b95b3b8d9d47f2e6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.2107",
    "kind": "arxiv",
    "version": 2
  }
}