Pith Number

pith:ACWAFTIC

pith:2020:ACWAFTICI45SDSCIXK3RWZCK3G

not attested not anchored not stored refs pending

Minimal Ramsey graphs with many vertices of small degree

Dennis Clemens, Pranshu Gupta, Simona Boyadzhiyska

arxiv:2009.04159 v1 · 2020-09-09 · 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{ACWAFTICI45SDSCIXK3RWZCK3G}

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	2026-07-05T01:34:15.339842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00ac02cd02473b21c848bab71b644ad9b4eb9c6f713075b9fb7db795cec5b486

Aliases

arxiv: 2009.04159 · arxiv_version: 2009.04159v1 · doi: 10.48550/arxiv.2009.04159 · pith_short_12: ACWAFTICI45S · pith_short_16: ACWAFTICI45SDSCI · pith_short_8: ACWAFTIC

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/ACWAFTICI45SDSCIXK3RWZCK3G \
  | 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: 00ac02cd02473b21c848bab71b644ad9b4eb9c6f713075b9fb7db795cec5b486

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd9290484b1e08343398679c1938d7088c1531d2ee4ccc8756b436f0c5a1f47a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-09-09T08:30:58Z",
    "title_canon_sha256": "0fba2f21d3e7bf9b9172c617439366624ae6b3ec696046c63bc325676949bd5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.04159",
    "kind": "arxiv",
    "version": 1
  }
}