Pith Number

pith:B7JJCDSC

pith:2011:B7JJCDSCSOAOUAIVWVNCNE5WYW

not attested not anchored not stored refs pending

Rank-one Characterization of Joint Spectral Radius of Finite Matrix Family

Jun Liu, Mingqing Xiao

arxiv:1109.1356 v8 · 2011-09-07 · math.NA · math.DS · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B7JJCDSCSOAOUAIVWVNCNE5WYW}

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	2026-05-18T00:53:51.772166Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fd2910e429380ea0115b55a2693b6c5a3e411d062cf459d274d1f6a53f19786

Aliases

arxiv: 1109.1356 · arxiv_version: 1109.1356v8 · doi: 10.48550/arxiv.1109.1356 · pith_short_12: B7JJCDSCSOAO · pith_short_16: B7JJCDSCSOAOUAIV · pith_short_8: B7JJCDSC

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/B7JJCDSCSOAOUAIVWVNCNE5WYW \
  | 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: 0fd2910e429380ea0115b55a2693b6c5a3e411d062cf459d274d1f6a53f19786

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49efa432637928003ff49792221f98f9394292d6754e17609ebe3a66be5903e8",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2011-09-07T05:16:06Z",
    "title_canon_sha256": "45a2eedb72d6c6ec6e6b8668635d74c8ff2c6129a613a6ab4e1392be6a05efcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.1356",
    "kind": "arxiv",
    "version": 8
  }
}