Pith Number

pith:IX4AMC6V

pith:2016:IX4AMC6VDLN5VJ4KKBKM6VBOTX

not attested not anchored not stored refs pending

The $(k,\ell)$-proper index of graphs

Colton Magnant, Hong Chang, Xueliang Li, Zhongmei Qin

arxiv:1606.03872 v2 · 2016-06-13 · 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{IX4AMC6VDLN5VJ4KKBKM6VBOTX}

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	2026-05-18T01:12:19.647523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45f8060bd51adbdaa78a5054cf542e9de367f07bc061ceec5eaae29c1012c35a

Aliases

arxiv: 1606.03872 · arxiv_version: 1606.03872v2 · doi: 10.48550/arxiv.1606.03872 · pith_short_12: IX4AMC6VDLN5 · pith_short_16: IX4AMC6VDLN5VJ4K · pith_short_8: IX4AMC6V

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/IX4AMC6VDLN5VJ4KKBKM6VBOTX \
  | 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: 45f8060bd51adbdaa78a5054cf542e9de367f07bc061ceec5eaae29c1012c35a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "966a8f257a66458785654374a357f54218bbde69b6ab82cb28de47fa12dcb3a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-13T09:30:48Z",
    "title_canon_sha256": "d0a5043793f62bd30cd2268a88e76e8e28028b494b16caaf16da2a3495120771"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03872",
    "kind": "arxiv",
    "version": 2
  }
}