Pith Number

pith:R7LKF2CF

pith:2010:R7LKF2CFFLK5RAEOND5IGLWS6E

not attested not anchored not stored refs pending

Schaefer's theorem for graphs

Manuel Bodirsky, Michael Pinsker

arxiv:1011.2894 v5 · 2010-11-12 · cs.CC · math.CO · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R7LKF2CFFLK5RAEOND5IGLWS6E}

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	2026-05-18T02:07:32.638701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8fd6a2e8452ad5d8808e68fa832ed2f1319607f59025a26ec1a5eee2c0d71707

Aliases

arxiv: 1011.2894 · arxiv_version: 1011.2894v5 · doi: 10.48550/arxiv.1011.2894 · pith_short_12: R7LKF2CFFLK5 · pith_short_16: R7LKF2CFFLK5RAEO · pith_short_8: R7LKF2CF

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/R7LKF2CFFLK5RAEOND5IGLWS6E \
  | 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: 8fd6a2e8452ad5d8808e68fa832ed2f1319607f59025a26ec1a5eee2c0d71707

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82e823d5b2ab6c0f8fc9f7d704b37e289e4a911b2beb27c5562a0ecd5edd1e91",
    "cross_cats_sorted": [
      "math.CO",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2010-11-12T12:15:48Z",
    "title_canon_sha256": "2aa082e433eb0fd5e64ad2c30c365ad3d7c59813df23d1bd39c5efec3dfc6f2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2894",
    "kind": "arxiv",
    "version": 5
  }
}