Pith Number

pith:M4HKAJ22

pith:2010:M4HKAJ22AYOJSCUCCI3U3BXYVT

not attested not anchored not stored refs pending

Factorization and dilation problems for completely positive maps on von Neumann algebras

Magdalena Musat, Uffe Haagerup

arxiv:1009.0778 v1 · 2010-09-03 · math.OA · 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{M4HKAJ22AYOJSCUCCI3U3BXYVT}

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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	2026-05-18T02:05:36.993369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

670ea0275a061c990a8212374d86f8aced2605f7322b3bf3adcaa65f3fd3e640

Aliases

arxiv: 1009.0778 · arxiv_version: 1009.0778v1 · doi: 10.48550/arxiv.1009.0778 · pith_short_12: M4HKAJ22AYOJ · pith_short_16: M4HKAJ22AYOJSCUC · pith_short_8: M4HKAJ22

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/M4HKAJ22AYOJSCUCCI3U3BXYVT \
  | 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: 670ea0275a061c990a8212374d86f8aced2605f7322b3bf3adcaa65f3fd3e640

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dbd93e1bfe5381572c2fa95a3a03fb96bd1134856c5c4c3a4ae33c84a28ee14",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-09-03T21:52:40Z",
    "title_canon_sha256": "0038d50ebba64b6681c06073239cf0c88e83e297792506323a54572d79815319"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0778",
    "kind": "arxiv",
    "version": 1
  }
}