Pith Number

pith:TB45YSJL

pith:2013:TB45YSJLA5DXI6JAVYJCT6QTF3

not attested not anchored not stored refs pending

On the largest graph-Lagrangians of hypergraphs

Cheng Zhao, Qingsong Tang, Xiangde Zhang, Yuejian Peng

arxiv:1311.1062 v2 · 2013-11-05 · 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{TB45YSJLA5DXI6JAVYJCT6QTF3}

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	2026-05-18T02:44:31.728279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9879dc492b0747747920ae1229fa132ed36f40023bde9d7651148c2d227027ad

Aliases

arxiv: 1311.1062 · arxiv_version: 1311.1062v2 · doi: 10.48550/arxiv.1311.1062 · pith_short_12: TB45YSJLA5DX · pith_short_16: TB45YSJLA5DXI6JA · pith_short_8: TB45YSJL

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/TB45YSJLA5DXI6JAVYJCT6QTF3 \
  | 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: 9879dc492b0747747920ae1229fa132ed36f40023bde9d7651148c2d227027ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "103ad819378daa06ae82eaf613fdc9906c8e7d8e052c143fc36fb2d2b5cf1e57",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-05T14:23:00Z",
    "title_canon_sha256": "fdf5fe981a663597e4be8606030a042115cc443b7937a980e2150ea49762873f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1062",
    "kind": "arxiv",
    "version": 2
  }
}