Pith Number

pith:O2WAAIAL

pith:2022:O2WAAIALZV7M7XYQVBPCHQY2MS

not attested not anchored not stored refs pending

A new upper bound on the minimum degree of minimal Ramsey graphs

Anurag Bishnoi, Thomas Lesgourgues

arxiv:2209.05147 v2 · 2022-09-12 · 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{O2WAAIALZV7M7XYQVBPCHQY2MS}

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	2026-07-05T08:42:20.363388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76ac00200bcd7ecfdf10a85e23c31a649d909757d271a0fc5a65c7ea19b19892

Aliases

arxiv: 2209.05147 · arxiv_version: 2209.05147v2 · doi: 10.48550/arxiv.2209.05147 · pith_short_12: O2WAAIALZV7M · pith_short_16: O2WAAIALZV7M7XYQ · pith_short_8: O2WAAIAL

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/O2WAAIALZV7M7XYQVBPCHQY2MS \
  | 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: 76ac00200bcd7ecfdf10a85e23c31a649d909757d271a0fc5a65c7ea19b19892

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f1ae0ce658fd85c394bd9d933332ee5f78e7fcf50490614b334d0c3c3de5693",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-09-12T11:06:15Z",
    "title_canon_sha256": "f31a8a0b8c0c88ec3dc3a83aaa705f2738dee1d5c80b860cf91c124477f47e4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.05147",
    "kind": "arxiv",
    "version": 2
  }
}