Pith Number

pith:ESAK2R7W

pith:2015:ESAK2R7W263YEOEL2JTFDO5OHI

not attested not anchored not stored refs pending

On the spectral radius of simple digraphs with prescribed number of arcs

Xiao-Dong Zhang, Ya-Lei Jin

arxiv:1509.07372 v1 · 2015-09-24 · 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{ESAK2R7W263YEOEL2JTFDO5OHI}

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	2026-05-18T01:32:09.158131Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2480ad47f6d7b782388bd26651bbae3a11c6c815f5a74d19955d7abdafc80a9b

Aliases

arxiv: 1509.07372 · arxiv_version: 1509.07372v1 · doi: 10.48550/arxiv.1509.07372 · pith_short_12: ESAK2R7W263Y · pith_short_16: ESAK2R7W263YEOEL · pith_short_8: ESAK2R7W

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/ESAK2R7W263YEOEL2JTFDO5OHI \
  | 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: 2480ad47f6d7b782388bd26651bbae3a11c6c815f5a74d19955d7abdafc80a9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2968c4b55b279dedbdd7492b87ea45780dfcf13f20558ccb86559fa4f235121f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-24T13:48:19Z",
    "title_canon_sha256": "0223d8b14b4900a1ecbf69bcb8453ec2ad5c37b96ab589038f576a638b9a442e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07372",
    "kind": "arxiv",
    "version": 1
  }
}