Pith Number

pith:MW4LNQRW

pith:2010:MW4LNQRWXKFWACHKYEK3FKXLT6

not attested not anchored not stored refs pending

Closed formula for the relative entropy of entanglement in all dimensions

Gilad Gour, Shmuel Friedland

arxiv:1007.4544 v2 · 2010-07-26 · quant-ph · 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{MW4LNQRWXKFWACHKYEK3FKXLT6}

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	2026-05-18T04:20:51.236141Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65b8b6c236ba8b6008eac115b2aaeb9fb55293c66b8d0edc3089c81a836ecb0a

Aliases

arxiv: 1007.4544 · arxiv_version: 1007.4544v2 · doi: 10.48550/arxiv.1007.4544 · pith_short_12: MW4LNQRWXKFW · pith_short_16: MW4LNQRWXKFWACHK · pith_short_8: MW4LNQRW

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/MW4LNQRWXKFWACHKYEK3FKXLT6 \
  | 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: 65b8b6c236ba8b6008eac115b2aaeb9fb55293c66b8d0edc3089c81a836ecb0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc82b97e78f7dd7969f786bd2d5089d7b65c4756514fca1d1897d6cff02482bb",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2010-07-26T19:50:20Z",
    "title_canon_sha256": "1a1e4e58e9957aac071a304cc3e26d603df74fc911a0b5c5d4b5862a8cd89579"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4544",
    "kind": "arxiv",
    "version": 2
  }
}