Pith Number

pith:UO3JTZQP

pith:2015:UO3JTZQP5QNZFSZPRBV662SRUV

not attested not anchored not stored refs pending

New Lower Bounds for 28 Classical Ramsey Numbers

Geoffrey Exoo, Milos Tatarevic

arxiv:1504.02403 v3 · 2015-04-09 · 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{UO3JTZQP5QNZFSZPRBV662SRUV}

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	2026-05-18T01:36:38.242310Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3b699e60fec1b92cb2f886bef6a51a5589a2955b912cb180747c6698a2babc8

Aliases

arxiv: 1504.02403 · arxiv_version: 1504.02403v3 · doi: 10.48550/arxiv.1504.02403 · pith_short_12: UO3JTZQP5QNZ · pith_short_16: UO3JTZQP5QNZFSZP · pith_short_8: UO3JTZQP

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/UO3JTZQP5QNZFSZPRBV662SRUV \
  | 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: a3b699e60fec1b92cb2f886bef6a51a5589a2955b912cb180747c6698a2babc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8692ca674dfa14cc90697d8b3da1834e9eed27f16bcc52a5f9a90a28be52653",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-04-09T17:58:49Z",
    "title_canon_sha256": "87a99842c5fbea6c62c7f28e8b0f40f9e81604cd1ab52205fd5820b731458566"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.02403",
    "kind": "arxiv",
    "version": 3
  }
}