Pith Number

pith:3GWWXDHH

pith:2010:3GWWXDHHBYBWM3W6HAFSPJDJSV

not attested not anchored not stored refs pending

Completely positive mappings and mean matrices

Adam Besenyei, Denes Petz

arxiv:1012.4754 v1 · 2010-12-21 · 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{3GWWXDHHBYBWM3W6HAFSPJDJSV}

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	2026-05-18T04:32:53.760920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9ad6b8ce70e03666ede380b27a4699555ad2f4b1d3400b543f887cb6e8420ff

Aliases

arxiv: 1012.4754 · arxiv_version: 1012.4754v1 · doi: 10.48550/arxiv.1012.4754 · pith_short_12: 3GWWXDHHBYBW · pith_short_16: 3GWWXDHHBYBWM3W6 · pith_short_8: 3GWWXDHH

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/3GWWXDHHBYBWM3W6HAFSPJDJSV \
  | 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: d9ad6b8ce70e03666ede380b27a4699555ad2f4b1d3400b543f887cb6e8420ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "946c9710ef8172b18105b8fe14287280685c1d57c10526cddf4edb6f0216e2af",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-12-21T18:16:56Z",
    "title_canon_sha256": "07c30122679f3ac4d5c557c1eb6e676ee647510c654b6f204b5962ca37206f80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4754",
    "kind": "arxiv",
    "version": 1
  }
}