Pith Number

pith:6KJ4VSQW

pith:2008:6KJ4VSQWR6NRRNHGNLOIAKKYR3

not attested not anchored not stored refs pending

Counting cocircuits and convex two-colourings is #P-complete

Andrew J. Goodall, Steven D. Noble

arxiv:0810.2042 v1 · 2008-10-11 · math.CO · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6KJ4VSQWR6NRRNHGNLOIAKKYR3}

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	2026-05-18T00:52:24.420305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f293caca168f9b18b4e66adc8029588ee37d158684537604779f1c40903c5484

Aliases

arxiv: 0810.2042 · arxiv_version: 0810.2042v1 · doi: 10.48550/arxiv.0810.2042 · pith_short_12: 6KJ4VSQWR6NR · pith_short_16: 6KJ4VSQWR6NRRNHG · pith_short_8: 6KJ4VSQW

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/6KJ4VSQWR6NRRNHGNLOIAKKYR3 \
  | 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: f293caca168f9b18b4e66adc8029588ee37d158684537604779f1c40903c5484

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d49edf547082114f3490345c6722f5515960f56ee1815efe89ba3a0dee900a8",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-10-11T17:11:35Z",
    "title_canon_sha256": "b237383b418297c4411084ebb2e90bc572fd2e52b51813768e2e84ce1e99e0d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.2042",
    "kind": "arxiv",
    "version": 1
  }
}