Pith Number

pith:WMNZQL3X

pith:2011:WMNZQL3XOHTJYMHC6NS3J4QUY4

not attested not anchored not stored refs pending

Vertices Belonging to All Critical Independent Sets of a Graph

Eugen Mandrescu, Vadim E. Levit

arxiv:1102.0401 v2 · 2011-02-02 · cs.DM · 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{WMNZQL3XOHTJYMHC6NS3J4QUY4}

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	2026-05-18T04:29:55.221665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b31b982f7771e69c30e2f365b4f214c71109a38501f4e1560f60850d6f7bb004

Aliases

arxiv: 1102.0401 · arxiv_version: 1102.0401v2 · doi: 10.48550/arxiv.1102.0401 · pith_short_12: WMNZQL3XOHTJ · pith_short_16: WMNZQL3XOHTJYMHC · pith_short_8: WMNZQL3X

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/WMNZQL3XOHTJYMHC6NS3J4QUY4 \
  | 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: b31b982f7771e69c30e2f365b4f214c71109a38501f4e1560f60850d6f7bb004

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1096bffb096feece485171f0112b6c0a8550cd92286d97eb8746b592d587f0d3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2011-02-02T10:58:35Z",
    "title_canon_sha256": "57fa9f01cf2e1dd1445752dbc4905a865705395b58e0851c864ba8f0f999c235"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0401",
    "kind": "arxiv",
    "version": 2
  }
}