Pith Number

pith:TILHKT2X

pith:2009:TILHKT2XPKV3IO6MZ7TM5ZD2CH

not attested not anchored not stored refs pending

Quantum mutual independence

Andreas Winter, Jonathan Oppenheim, Michal Horodecki

arxiv:0902.0912 v2 · 2009-02-05 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TILHKT2XPKV3IO6MZ7TM5ZD2CH}

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	2026-07-04T16:21:40.478391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a16754f577aabb43bcccfe6cee47a11cefcb1148998d3de9dfe4a94940d0059

Aliases

arxiv: 0902.0912 · arxiv_version: 0902.0912v2 · doi: 10.48550/arxiv.0902.0912 · pith_short_12: TILHKT2XPKV3 · pith_short_16: TILHKT2XPKV3IO6M · pith_short_8: TILHKT2X

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/TILHKT2XPKV3IO6MZ7TM5ZD2CH \
  | 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: 9a16754f577aabb43bcccfe6cee47a11cefcb1148998d3de9dfe4a94940d0059

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d1385d02e6b26236688cbdd55764fd0392905aab861cbfa372516c3c09fd54a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2009-02-05T14:36:34Z",
    "title_canon_sha256": "241147e506eee8422f9cf541fcbe2ac9cdfdfda10a3b8676910835d6bf9edb58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.0912",
    "kind": "arxiv",
    "version": 2
  }
}