Pith Number

pith:Q7XAF5RI

pith:2009:Q7XAF5RIRINZLBUZVKRBGTPALW

not attested not anchored not stored refs pending

Higher rank numerical ranges of normal matrices

Chi-Kwong Li, Hwa-Long Gau, Nung-sing Sze, Yiu-Tung Poon

arxiv:0902.4869 v2 · 2009-02-27 · math.FA · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q7XAF5RIRINZLBUZVKRBGTPALW}

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	2026-05-18T04:29:44.685983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87ee02f6288a1b958699aaa2134de05dacb7de3a337b1c87e2f1d377919935f3

Aliases

arxiv: 0902.4869 · arxiv_version: 0902.4869v2 · doi: 10.48550/arxiv.0902.4869 · pith_short_12: Q7XAF5RIRINZ · pith_short_16: Q7XAF5RIRINZLBUZ · pith_short_8: Q7XAF5RI

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/Q7XAF5RIRINZLBUZVKRBGTPALW \
  | 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: 87ee02f6288a1b958699aaa2134de05dacb7de3a337b1c87e2f1d377919935f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be98cd82141c418f5d30fb5b9543847641e08e4b4a73cb27626dc870cff10e2a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-02-27T16:50:50Z",
    "title_canon_sha256": "040c3904be03370b992cf32abf11d8b877317d727aa04cef1d79bd7e09dee5f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.4869",
    "kind": "arxiv",
    "version": 2
  }
}