Pith Number

pith:DFXTNVZ4

pith:2007:DFXTNVZ4XZLIYYEROQQFXQGXEC

not attested not anchored not stored refs pending

More spectral bounds on the clique and independence numbers

Vladimir Nikiforov

arxiv:0706.0548 v2 · 2007-06-04 · 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{DFXTNVZ4XZLIYYEROQQFXQGXEC}

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	2026-05-18T00:51:58.708357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

196f36d73cbe568c609174205bc0d7209fd3097fc75dc2a43a7f73c26d7fd49f

Aliases

arxiv: 0706.0548 · arxiv_version: 0706.0548v2 · doi: 10.48550/arxiv.0706.0548 · pith_short_12: DFXTNVZ4XZLI · pith_short_16: DFXTNVZ4XZLIYYER · pith_short_8: DFXTNVZ4

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/DFXTNVZ4XZLIYYEROQQFXQGXEC \
  | 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: 196f36d73cbe568c609174205bc0d7209fd3097fc75dc2a43a7f73c26d7fd49f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be13bf1a0b074773c50c7938db4617821b5953b75862b1d201bf5df9f5c7f4f0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-06-04T22:00:02Z",
    "title_canon_sha256": "922e80b823f2f5edd3d9c24bae5a0fc311fd7ffa9664657d2e587f6a44f107f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.0548",
    "kind": "arxiv",
    "version": 2
  }
}