Pith Number

pith:E377HLW7

pith:2019:E377HLW7CFZ5JU3O2AYXDQYV3W

not attested not anchored not stored refs pending

Lower Bounds for Small Ramsey Numbers on Hypergraphs

S. Cliff Liu

arxiv:1906.00132 v2 · 2019-06-01 · 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{E377HLW7CFZ5JU3O2AYXDQYV3W}

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	2026-07-04T23:50:19.049178Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26fff3aedf1173d4d36ed03171c315ddbf57ebd593dc5e3ff6411b19e3a70996

Aliases

arxiv: 1906.00132 · arxiv_version: 1906.00132v2 · doi: 10.48550/arxiv.1906.00132 · pith_short_12: E377HLW7CFZ5 · pith_short_16: E377HLW7CFZ5JU3O · pith_short_8: E377HLW7

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/E377HLW7CFZ5JU3O2AYXDQYV3W \
  | 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: 26fff3aedf1173d4d36ed03171c315ddbf57ebd593dc5e3ff6411b19e3a70996

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c30aee259a9e3b933f0b19acd800b5ee88c87b35087366f6b7cc21c6fdf15dc0",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-06-01T02:38:22Z",
    "title_canon_sha256": "42b2a6625501e2dc9fc66916252a1801883bdbfa546226123e2740e091555a90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.00132",
    "kind": "arxiv",
    "version": 2
  }
}