Pith Number

pith:QL6GEUP4

pith:2011:QL6GEUP46XW5CZBMVWJVO7RW5H

not attested not anchored not stored refs pending

Bounds on Shannon Capacity and Ramsey Numbers from Product of Graphs

Stanis{\l}aw Radziszowski, Xiaodong Xu

arxiv:1201.0304 v2 · 2011-12-31 · math.CO · cs.IT · 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{QL6GEUP46XW5CZBMVWJVO7RW5H}

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	2026-05-18T02:50:52.175557Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82fc6251fcf5edd1642cad93577e36e9c21fb8e139531d44908ffea00bc9f1d2

Aliases

arxiv: 1201.0304 · arxiv_version: 1201.0304v2 · doi: 10.48550/arxiv.1201.0304 · pith_short_12: QL6GEUP46XW5 · pith_short_16: QL6GEUP46XW5CZBM · pith_short_8: QL6GEUP4

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/QL6GEUP46XW5CZBMVWJVO7RW5H \
  | 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: 82fc6251fcf5edd1642cad93577e36e9c21fb8e139531d44908ffea00bc9f1d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15e8a5d71c65735da24d92c3a89a7abda3f14957f72ecb1b84f2cadbf4649aba",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-31T19:11:42Z",
    "title_canon_sha256": "37deb8e93b744f98c442fe17626f0fd16135d399edfc4439671c8c92b10b36ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0304",
    "kind": "arxiv",
    "version": 2
  }
}