Pith Number

pith:MRNY7UWD

pith:2014:MRNY7UWDVYLM5QZ7RTZQRGY7YH

not attested not anchored not stored refs pending

Spectral Radius of Bipartite Graphs

Chia-an Liu, Chih-wen Weng

arxiv:1402.5621 v1 · 2014-02-23 · 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{MRNY7UWDVYLM5QZ7RTZQRGY7YH}

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	2026-05-18T02:58:14.271740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

645b8fd2c3ae16cec33f8cf3089b1fc1cf1e3c3e6647cba4172cb95eeef6cd61

Aliases

arxiv: 1402.5621 · arxiv_version: 1402.5621v1 · doi: 10.48550/arxiv.1402.5621 · pith_short_12: MRNY7UWDVYLM · pith_short_16: MRNY7UWDVYLM5QZ7 · pith_short_8: MRNY7UWD

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/MRNY7UWDVYLM5QZ7RTZQRGY7YH \
  | 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: 645b8fd2c3ae16cec33f8cf3089b1fc1cf1e3c3e6647cba4172cb95eeef6cd61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d0d1964deb07367372324e64a4e2611e682bd00f2e8c0fad3ee5d1306030e2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-02-23T15:56:36Z",
    "title_canon_sha256": "ca2946691cbb2080d4234f2d6e894349d7fb37e9c75d02903b766c78d696a489"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.5621",
    "kind": "arxiv",
    "version": 1
  }
}