Pith Number

pith:SWKPV6TK

pith:2010:SWKPV6TKSY64Z5RE2HCEF3VV62

not attested not anchored not stored refs pending

Numerical shadows: measures and densities on the numerical range

Charles F. Dunkl, John A. Holbrook, Karol \.Zyczkowski, Piotr Gawron, Zbigniew Pucha{\l}a

arxiv:1010.4189 v1 · 2010-10-20 · math.FA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SWKPV6TKSY64Z5RE2HCEF3VV62}

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	2026-05-18T04:16:02.286619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9594fafa6a963dccf624d1c442eeb5f698dd31138d857da9555d5d841e7f8a6b

Aliases

arxiv: 1010.4189 · arxiv_version: 1010.4189v1 · doi: 10.48550/arxiv.1010.4189 · pith_short_12: SWKPV6TKSY64 · pith_short_16: SWKPV6TKSY64Z5RE · pith_short_8: SWKPV6TK

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/SWKPV6TKSY64Z5RE2HCEF3VV62 \
  | 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: 9594fafa6a963dccf624d1c442eeb5f698dd31138d857da9555d5d841e7f8a6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ad18d6f885320e7b9dbb04df111d23a2e75ba9f9cb5075c364dcbd6c46f9216",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-10-20T13:11:28Z",
    "title_canon_sha256": "3408392f051e76643184b2d6258beb22fcc6304b517bb5b5d124a89d1284e30f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4189",
    "kind": "arxiv",
    "version": 1
  }
}