Pith Number

pith:T4WUKMLX

pith:2013:T4WUKMLXMF5SXJZDKLXAY7ZOFU

not attested not anchored not stored refs pending

Minimum vertex cover problems on random hypergraphs: replica symmetric solution and a leaf removal algorithm

Koji Hukushima, Satoshi Takabe

arxiv:1301.5769 v1 · 2013-01-24 · cond-mat.dis-nn · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T4WUKMLXMF5SXJZDKLXAY7ZOFU}

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	2026-05-18T02:48:27.475855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f2d453177617b2ba72352ee0c7f2e2d1b8d77c6ef9429d7d910d4192767c293

Aliases

arxiv: 1301.5769 · arxiv_version: 1301.5769v1 · doi: 10.48550/arxiv.1301.5769 · pith_short_12: T4WUKMLXMF5S · pith_short_16: T4WUKMLXMF5SXJZD · pith_short_8: T4WUKMLX

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/T4WUKMLXMF5SXJZDKLXAY7ZOFU \
  | 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: 9f2d453177617b2ba72352ee0c7f2e2d1b8d77c6ef9429d7d910d4192767c293

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c8e7ba9b1e87a90ac496d3ea0cd8a4f69dabdff001e02c328236e4ae3ba25f7",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2013-01-24T12:24:06Z",
    "title_canon_sha256": "20c6f0f7404a953ac7e6ac0a8f13216be430b70472d9c7619bc86dac5f4cea36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.5769",
    "kind": "arxiv",
    "version": 1
  }
}