Pith Number

pith:77WTCJR4

pith:2017:77WTCJR4HAYYKS7NTIBON5QP4J

not attested not anchored not stored refs pending

A branch-and-price approach with MILP formulation to modularity density maximization on graphs

Keisuke Sato, Yoichi Izunaga

arxiv:1705.02961 v3 · 2017-05-08 · cs.SI · cs.DM · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{77WTCJR4HAYYKS7NTIBON5QP4J}

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	2026-05-18T00:41:33.014998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffed31263c3831854bed9a02e6f60fe25050c93a22e3280f96485eee032ff735

Aliases

arxiv: 1705.02961 · arxiv_version: 1705.02961v3 · doi: 10.48550/arxiv.1705.02961 · pith_short_12: 77WTCJR4HAYY · pith_short_16: 77WTCJR4HAYYKS7N · pith_short_8: 77WTCJR4

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/77WTCJR4HAYYKS7NTIBON5QP4J \
  | 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: ffed31263c3831854bed9a02e6f60fe25050c93a22e3280f96485eee032ff735

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e99257ab236c1f8d8f9ae1d097cb60c873c74cc6ad381161529622d4ab59d53",
    "cross_cats_sorted": [
      "cs.DM",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SI",
    "submitted_at": "2017-05-08T16:37:00Z",
    "title_canon_sha256": "f6cf00e6a927da2bd29bbb1aa983cbd2348aef49c1ff569f679df7079db950b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.02961",
    "kind": "arxiv",
    "version": 3
  }
}