Pith Number

pith:NA7N33BF

pith:2009:NA7N33BF3IKVQJ65GD4QKZZ7BS

not attested not anchored not stored refs pending

Uniform Semiclassical Approximation for the Wigner $6j$ Symbol in Terms of Rotation Matrices

Liang Yu, Robert G. Littlejohn

arxiv:0905.4240 v2 · 2009-05-26 · 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{NA7N33BF3IKVQJ65GD4QKZZ7BS}

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	2026-05-18T02:13:31.890519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

683eddec25da155827dd30f905673f0ca3117d96022bfbbf2b640c19f197c202

Aliases

arxiv: 0905.4240 · arxiv_version: 0905.4240v2 · doi: 10.48550/arxiv.0905.4240 · pith_short_12: NA7N33BF3IKV · pith_short_16: NA7N33BF3IKVQJ65 · pith_short_8: NA7N33BF

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/NA7N33BF3IKVQJ65GD4QKZZ7BS \
  | 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: 683eddec25da155827dd30f905673f0ca3117d96022bfbbf2b640c19f197c202

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "347cf653c8a1b85d26985a99f91bd5ea73c781683575ff02c29ff2ddf41dfe98",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-05-26T16:56:24Z",
    "title_canon_sha256": "a384ff7fc7a135f632d752e27c139c1bce39bcaecdafa7f942276cb75bd0d6a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.4240",
    "kind": "arxiv",
    "version": 2
  }
}