Pith Number

pith:MWNHN6QI

pith:2012:MWNHN6QIJL5EYLZAFS6RP7ZAU4

not attested not anchored not stored refs pending

Sparseness of 4-cycle systems

Hung-Lin Fu, Shung-Liang Wu, Yuichiro Fujiwara

arxiv:1209.4438 v1 · 2012-09-20 · 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{MWNHN6QIJL5EYLZAFS6RP7ZAU4}

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	2026-05-18T03:45:11.732923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

659a76fa084afa4c2f202cbd17ff20a72a537f355c14c66a30acf6036ac33185

Aliases

arxiv: 1209.4438 · arxiv_version: 1209.4438v1 · doi: 10.48550/arxiv.1209.4438 · pith_short_12: MWNHN6QIJL5E · pith_short_16: MWNHN6QIJL5EYLZA · pith_short_8: MWNHN6QI

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/MWNHN6QIJL5EYLZAFS6RP7ZAU4 \
  | 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: 659a76fa084afa4c2f202cbd17ff20a72a537f355c14c66a30acf6036ac33185

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "808593bec0a9aafab9ec4b384fff4355b52652de52467a0d6ce18edf7a183a06",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-20T06:52:26Z",
    "title_canon_sha256": "10cc09c30b497c45eafa28035bbccd8300c7587140735e704998b097e8081453"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4438",
    "kind": "arxiv",
    "version": 1
  }
}