Pith Number

pith:4FX7YD26

pith:2020:4FX7YD26DU546L32WLNVT3AC3L

not attested not anchored not stored refs pending

The minimum degree of minimal Ramsey graphs for cliques

Anurag Bishnoi, John Bamberg, Thomas Lesgourgues

arxiv:2008.02474 v5 · 2020-08-06 · 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{4FX7YD26DU546L32WLNVT3AC3L}

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	2026-07-05T05:09:11.138527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e16ffc0f5e1d3bcf2f7ab2db59ec02daee567b5cde6e6408db267b3221eec7dc

Aliases

arxiv: 2008.02474 · arxiv_version: 2008.02474v5 · doi: 10.48550/arxiv.2008.02474 · pith_short_12: 4FX7YD26DU54 · pith_short_16: 4FX7YD26DU546L32 · pith_short_8: 4FX7YD26

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/4FX7YD26DU546L32WLNVT3AC3L \
  | 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: e16ffc0f5e1d3bcf2f7ab2db59ec02daee567b5cde6e6408db267b3221eec7dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20e95ca2a79e591f7348f18e124f447df8f2a084c960723d4887d81fff9a1f8c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-08-06T06:38:46Z",
    "title_canon_sha256": "244b6a923694c5a3ba39cd6c8c191157364134f8678ad56f824059cf1d3243e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2008.02474",
    "kind": "arxiv",
    "version": 5
  }
}