Pith Number

pith:WXIOIYGZ

pith:2013:WXIOIYGZP7YEBRJKS5FJZECJZC

not attested not anchored not stored refs pending

Von Neumann entropy and majorization

Paul Busch, Yuan Li

arxiv:1304.7442 v2 · 2013-04-28 · math-ph · math.MP · 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{WXIOIYGZP7YEBRJKS5FJZECJZC}

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	2026-05-18T03:12:57.605730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5d0e460d97ff040c52a974a9c9049c8bfc923c25f54f986b4ac309d17b49cd6

Aliases

arxiv: 1304.7442 · arxiv_version: 1304.7442v2 · doi: 10.48550/arxiv.1304.7442 · pith_short_12: WXIOIYGZP7YE · pith_short_16: WXIOIYGZP7YEBRJK · pith_short_8: WXIOIYGZ

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/WXIOIYGZP7YEBRJKS5FJZECJZC \
  | 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: b5d0e460d97ff040c52a974a9c9049c8bfc923c25f54f986b4ac309d17b49cd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1f962e6dda0d1479a599420815bc35a3464c8d980e8abb307e70e230bf6d136",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-04-28T08:12:08Z",
    "title_canon_sha256": "0c5bb9d02b7d82ec1e9f6aa228989b11dbd7f0616f8d6fa595833fe845711581"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.7442",
    "kind": "arxiv",
    "version": 2
  }
}