Pith Number

pith:CCCLEPH6

pith:2015:CCCLEPH63ME4CJPTXJEMXUBHPE

not attested not anchored not stored refs pending

The complexity of approximately counting in 2-spin systems on $k$-uniform bounded-degree hypergraphs

Andreas Galanis, Leslie Ann Goldberg

arxiv:1505.06146 v4 · 2015-05-22 · cs.CC · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CCCLEPH63ME4CJPTXJEMXUBHPE}

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	2026-05-18T01:12:18.452351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1084b23cfedb09c125f3ba48cbd027790e62d311becb223df4e1174b12087a2b

Aliases

arxiv: 1505.06146 · arxiv_version: 1505.06146v4 · doi: 10.48550/arxiv.1505.06146 · pith_short_12: CCCLEPH63ME4 · pith_short_16: CCCLEPH63ME4CJPT · pith_short_8: CCCLEPH6

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/CCCLEPH63ME4CJPTXJEMXUBHPE \
  | 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: 1084b23cfedb09c125f3ba48cbd027790e62d311becb223df4e1174b12087a2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf96623fe656548a146605d1d995a6ee3875c25e59b0d506f81b957aac0df2bf",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-05-22T17:00:46Z",
    "title_canon_sha256": "3f83700cc129252574dc37ebc457ec7e4642863abe726c61ba283da1de70d7e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.06146",
    "kind": "arxiv",
    "version": 4
  }
}