Pith Number

pith:NAX3UF5C

pith:2012:NAX3UF5CFKNP2SBIATMAX2NRR6

not attested not anchored not stored refs pending

Joint numerical ranges, quantum maps, and joint numerical shadows

Eugene Gutkin, Karol Zyczkowski

arxiv:1207.1227 v2 · 2012-07-05 · quant-ph · math-ph · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NAX3UF5CFKNP2SBIATMAX2NRR6}

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	2026-05-18T03:33:25.899783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

682fba17a22a9afd482804d80be9b18f8d2957e3d120513346e138c2bc5ffe54

Aliases

arxiv: 1207.1227 · arxiv_version: 1207.1227v2 · doi: 10.48550/arxiv.1207.1227 · pith_short_12: NAX3UF5CFKNP · pith_short_16: NAX3UF5CFKNP2SBI · pith_short_8: NAX3UF5C

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/NAX3UF5CFKNP2SBIATMAX2NRR6 \
  | 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: 682fba17a22a9afd482804d80be9b18f8d2957e3d120513346e138c2bc5ffe54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "126b2587d84f364d21ed87cd035bae4b08e87b39b4ed6b94f113fa5e67d09870",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2012-07-05T11:22:19Z",
    "title_canon_sha256": "07c4333bccb59370006033ab47b67fddc005792d48601f5cbaf89eb3a17a560b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1227",
    "kind": "arxiv",
    "version": 2
  }
}