Pith Number

pith:XKM776X3

pith:2006:XKM776X3ZLHSRPBAEYDEXRT52F

not attested not anchored not stored refs pending

The Shannon capacity of a graph and the independence numbers of its powers

Eyal Lubetzky, Noga Alon

arxiv:cs/0608021 v1 · 2006-08-03 · cs.IT · cs.DM · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XKM776X3ZLHSRPBAEYDEXRT52F}

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	2026-05-18T00:58:26.656626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba99fffafbcacf28bc2026064bc67dd141d2b7c523333b4bc738a5098ddc1957

Aliases

arxiv: cs/0608021 · arxiv_version: cs/0608021v1 · doi: 10.48550/arxiv.cs/0608021 · pith_short_12: XKM776X3ZLHS · pith_short_16: XKM776X3ZLHSRPBA · pith_short_8: XKM776X3

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/XKM776X3ZLHSRPBAEYDEXRT52F \
  | 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: ba99fffafbcacf28bc2026064bc67dd141d2b7c523333b4bc738a5098ddc1957

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13e5ad719634b37146306c51a4e204894d7d7b5e848f9d05ab5276c66b218805",
    "cross_cats_sorted": [
      "cs.DM",
      "math.IT"
    ],
    "license": "",
    "primary_cat": "cs.IT",
    "submitted_at": "2006-08-03T14:46:36Z",
    "title_canon_sha256": "6e0254964646979831e8981b6c8288cbea2db1967caf48b43ab30a5fe2d4d507"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cs/0608021",
    "kind": "arxiv",
    "version": 1
  }
}