Pith Number

pith:YFBIRRZO

pith:2011:YFBIRRZO44WN2BTNZYFLMVNU5I

not attested not anchored not stored refs pending

The Wigner 3n-j Graphs up to 12 Vertices

Richard J. Mathar

arxiv:1109.2358 v3 · 2011-09-11 · 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{YFBIRRZO44WN2BTNZYFLMVNU5I}

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	2026-05-18T04:03:42.927381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c14288c72ee72cdd066dce0ab655b4ea0d651c99f79660a1c61f3d408fa2f51a

Aliases

arxiv: 1109.2358 · arxiv_version: 1109.2358v3 · doi: 10.48550/arxiv.1109.2358 · pith_short_12: YFBIRRZO44WN · pith_short_16: YFBIRRZO44WN2BTN · pith_short_8: YFBIRRZO

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/YFBIRRZO44WN2BTNZYFLMVNU5I \
  | 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: c14288c72ee72cdd066dce0ab655b4ea0d651c99f79660a1c61f3d408fa2f51a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af4d4e52a2994d9e8336ebc8fc5ecaa5f159af86a01110512620c7b4793728e5",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-09-11T22:25:24Z",
    "title_canon_sha256": "bc1e6d719f326caa4a8af7c3f6899101e336c1e6880fee9a42b77be8949e0507"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2358",
    "kind": "arxiv",
    "version": 3
  }
}