Pith Number

pith:XD2F2ZW5

pith:2012:XD2F2ZW5AF2STVVYGCMUGWUJR3

not attested not anchored not stored refs pending

When do pieces determine the whole? Extremal marginals of a completely positive map

Erkka Haapasalo, Juha-Pekka Pellonp\"a\"a, Teiko Heinosaari

arxiv:1209.5933 v1 · 2012-09-26 · 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{XD2F2ZW5AF2STVVYGCMUGWUJR3}

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	2026-05-18T02:56:04.034635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8f45d66dd017529d6b83099435a898ee6957c28de1276ea98821072517db309

Aliases

arxiv: 1209.5933 · arxiv_version: 1209.5933v1 · doi: 10.48550/arxiv.1209.5933 · pith_short_12: XD2F2ZW5AF2S · pith_short_16: XD2F2ZW5AF2STVVY · pith_short_8: XD2F2ZW5

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/XD2F2ZW5AF2STVVYGCMUGWUJR3 \
  | 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: b8f45d66dd017529d6b83099435a898ee6957c28de1276ea98821072517db309

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b138c57be2fc500917f6c48bd973d5246f98a69b147676a60a6a26b6885f5e2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2012-09-26T13:26:11Z",
    "title_canon_sha256": "8ab2ab86b6a5646b27768d43183451015ee393dec7e203e1dfb04196b56d0c22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5933",
    "kind": "arxiv",
    "version": 1
  }
}