Pith Number

pith:SAO4YEYN

pith:2013:SAO4YEYNUZMCWA5XP33SXLCUWE

not attested not anchored not stored refs pending

The Complexity of Counting Homomorphisms to Cactus Graphs Modulo 2

Andreas G\"obel, David Richerby, Leslie Ann Goldberg

arxiv:1307.0556 v4 · 2013-07-01 · cs.CC · 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{SAO4YEYNUZMCWA5XP33SXLCUWE}

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	2026-05-18T02:41:58.391648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

901dcc130da6582b03b77ef72bac54b13be957de0461383d8c041009d4b42392

Aliases

arxiv: 1307.0556 · arxiv_version: 1307.0556v4 · doi: 10.48550/arxiv.1307.0556 · pith_short_12: SAO4YEYNUZMC · pith_short_16: SAO4YEYNUZMCWA5X · pith_short_8: SAO4YEYN

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/SAO4YEYNUZMCWA5XP33SXLCUWE \
  | 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: 901dcc130da6582b03b77ef72bac54b13be957de0461383d8c041009d4b42392

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82935e2046911d49d308ef58aab61302f6416e43ac0f71e76b2c345ea26ed135",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2013-07-01T23:02:31Z",
    "title_canon_sha256": "aedc8f8342ee88ab7d4a52491614b1e1419e09561e6317758c3a6dbc252e6f04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0556",
    "kind": "arxiv",
    "version": 4
  }
}