Pith Number

pith:Z2VHKLR5

pith:2000:Z2VHKLR5LBTLD4UTNHZR4JASVN

not attested not anchored not stored refs pending

Wigner Functions with Boundaries

Joao Nuno Prata, Nuno Costa Dias

arxiv:quant-ph/0012140 v2 · 2000-12-23 · 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{Z2VHKLR5LBTLD4UTNHZR4JASVN}

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	2026-05-18T01:38:02.908608Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceaa752e3d5866b1f29369f31e2412ab5136bf1c5b7e8e4792024f8c167e4f4f

Aliases

arxiv: quant-ph/0012140 · arxiv_version: quant-ph/0012140v2 · doi: 10.48550/arxiv.quant-ph/0012140 · pith_short_12: Z2VHKLR5LBTL · pith_short_16: Z2VHKLR5LBTLD4UT · pith_short_8: Z2VHKLR5

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/Z2VHKLR5LBTLD4UTNHZR4JASVN \
  | 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: ceaa752e3d5866b1f29369f31e2412ab5136bf1c5b7e8e4792024f8c167e4f4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52ef4251a5d8743f3fad09006573d447ff48b09c20acede32216ff46a0c4ea58",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2000-12-23T20:01:21Z",
    "title_canon_sha256": "bc63a3b1d2cd46e8d27d251dbf461fe74f4e05277ac06c5d81ebf78ba14622fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0012140",
    "kind": "arxiv",
    "version": 2
  }
}