Pith Number

pith:RGXUT7IU

pith:2016:RGXUT7IUPDNAB34GPBCOM65QE5

not attested not anchored not stored refs pending

A Sharp upper bound for the spectral radius of a nonnegative matrix and applications

Lihua You, Xiao-Dong Zhang, Yujie Shu

arxiv:1607.05883 v1 · 2016-07-20 · 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{RGXUT7IUPDNAB34GPBCOM65QE5}

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	2026-05-18T01:10:43.796252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89af49fd1478da00ef867844e67bb0276a2c54d7227d926e35124796501043bd

Aliases

arxiv: 1607.05883 · arxiv_version: 1607.05883v1 · doi: 10.48550/arxiv.1607.05883 · pith_short_12: RGXUT7IUPDNA · pith_short_16: RGXUT7IUPDNAB34G · pith_short_8: RGXUT7IU

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/RGXUT7IUPDNAB34GPBCOM65QE5 \
  | 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: 89af49fd1478da00ef867844e67bb0276a2c54d7227d926e35124796501043bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6d5c73fff2d1c8fd71c0b41c26adf033a4388c5fd73bf697867931c507ee1ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-07-20T09:23:31Z",
    "title_canon_sha256": "435f2c730a8a3496e4f37e299938fcc22a697428f17a05d274ac18d8f9e2d326"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.05883",
    "kind": "arxiv",
    "version": 1
  }
}