Pith Number

pith:DWM6O3KV

pith:2014:DWM6O3KVKRQSGT2AMPNQQZFG2L

not attested not anchored not stored refs pending

The spectrum of the product of operators, and the product of their numerical ranges

Chi-Kwong Li, Kuo-Zhong Wang, Ming-Cheng Tsai, Ngai-Ching Wong

arxiv:1404.5822 v2 · 2014-04-23 · 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{DWM6O3KVKRQSGT2AMPNQQZFG2L}

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	2026-05-18T02:47:43.985761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d99e76d555461234f4063db0864a6d2c3fc998e7b0fd67c58c781d8ca17b4f6

Aliases

arxiv: 1404.5822 · arxiv_version: 1404.5822v2 · doi: 10.48550/arxiv.1404.5822 · pith_short_12: DWM6O3KVKRQS · pith_short_16: DWM6O3KVKRQSGT2A · pith_short_8: DWM6O3KV

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/DWM6O3KVKRQSGT2AMPNQQZFG2L \
  | 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: 1d99e76d555461234f4063db0864a6d2c3fc998e7b0fd67c58c781d8ca17b4f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19b36af70b017a1b06d2058e0989df602fdd4efa2d479bec85dc4c623f278116",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-04-23T13:41:47Z",
    "title_canon_sha256": "e792bdd3e9de4c26302bef14271dc775235e8523bfcb5dd79833ce6ff363255f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.5822",
    "kind": "arxiv",
    "version": 2
  }
}