Pith Number

pith:GMRXJCZH

pith:2015:GMRXJCZHTDCNV774FQHXQDBBRO

not attested not anchored not stored refs pending

Sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix

Lihua You, Pingzhi Yuan, Yujie Shu

arxiv:1507.07059 v1 · 2015-07-25 · 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{GMRXJCZHTDCNV774FQHXQDBBRO}

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	2026-05-18T01:36:17.379096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3323748b2798c4dafffc2c0f780c218bb5a77851fda550f25ea62e3985b802f0

Aliases

arxiv: 1507.07059 · arxiv_version: 1507.07059v1 · doi: 10.48550/arxiv.1507.07059 · pith_short_12: GMRXJCZHTDCN · pith_short_16: GMRXJCZHTDCNV774 · pith_short_8: GMRXJCZH

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/GMRXJCZHTDCNV774FQHXQDBBRO \
  | 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: 3323748b2798c4dafffc2c0f780c218bb5a77851fda550f25ea62e3985b802f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "923c00524c4c201e4a2ae798409ccf2cbdeffeaadba28af4c724fb1a4c41a501",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-25T03:14:02Z",
    "title_canon_sha256": "2ce7f234e9ad452db4cd95b4d501e2544e2d4e830fa21dea697b48483309e635"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.07059",
    "kind": "arxiv",
    "version": 1
  }
}