Pith Number

pith:SOBITWPN

pith:2015:SOBITWPN5DCCOGJRONCCCBZ5Z7

not attested not anchored not stored refs pending

Numerical Ranges of the product of Operators

Chi-Kwong Li, Hongke Du, Kuo-Zhong Wang, Ning Zuo, Yueqing Wang

arxiv:1510.01672 v2 · 2015-10-06 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SOBITWPN5DCCOGJRONCCCBZ5Z7}

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	2026-05-18T01:05:12.706482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

938289d9ede8c4271931734421073dcfcc0e2de4a0a9d87ed9926de78a021f61

Aliases

arxiv: 1510.01672 · arxiv_version: 1510.01672v2 · doi: 10.48550/arxiv.1510.01672 · pith_short_12: SOBITWPN5DCC · pith_short_16: SOBITWPN5DCCOGJR · pith_short_8: SOBITWPN

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/SOBITWPN5DCCOGJRONCCCBZ5Z7 \
  | 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: 938289d9ede8c4271931734421073dcfcc0e2de4a0a9d87ed9926de78a021f61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b9173351a308e70992dcb0864750d15d61f7603799879765fef2cda40ecc63b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-10-06T17:21:49Z",
    "title_canon_sha256": "e278867fae3122a435f1f284a4e691ef62108c6cb374eeba594f08595e5340fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01672",
    "kind": "arxiv",
    "version": 2
  }
}