Pith Number

pith:BNSYBV7Z

pith:2012:BNSYBV7Z6VWV65C5WZMCF5PJST

not attested not anchored not stored refs pending

New Computational Upper Bounds for Ramsey Numbers R(3,k)

Jan Goedgebeur, Stanis{\l}aw P. Radziszowski

arxiv:1210.5826 v4 · 2012-10-22 · 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{BNSYBV7Z6VWV65C5WZMCF5PJST}

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	2026-05-18T03:30:25.504739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b6580d7f9f56d5f745db65822f5e994f3f65902067d3511c69bbe1053ee3117

Aliases

arxiv: 1210.5826 · arxiv_version: 1210.5826v4 · doi: 10.48550/arxiv.1210.5826 · pith_short_12: BNSYBV7Z6VWV · pith_short_16: BNSYBV7Z6VWV65C5 · pith_short_8: BNSYBV7Z

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/BNSYBV7Z6VWV65C5WZMCF5PJST \
  | 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: 0b6580d7f9f56d5f745db65822f5e994f3f65902067d3511c69bbe1053ee3117

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41b1ec6fde1eb5a4abcb8f72626d04943caf1659fdfdf9bdbac1619031a7b9ed",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-22T08:06:37Z",
    "title_canon_sha256": "f392b3f89bed9b5773168a354b79af0e7acf294b82c9ce202412589267d76c92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5826",
    "kind": "arxiv",
    "version": 4
  }
}