Pith Number

pith:XX7PSHWF

pith:2009:XX7PSHWFOUFDOLM5AMTV4Q7FUS

not attested not anchored not stored refs pending

Raising and lowering operators for angular momentum quantum numbers l in spherical harmonics

D. M. Xun, L. Shan, Q. H. Liu

arxiv:0912.5146 v1 · 2009-12-28 · 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{XX7PSHWFOUFDOLM5AMTV4Q7FUS}

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	2026-07-04T17:18:30.973997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdfef91ec5750a372d9d03275e43e5a4af6f63101080c5aafcbcfab282d45383

Aliases

arxiv: 0912.5146 · arxiv_version: 0912.5146v1 · doi: 10.48550/arxiv.0912.5146 · pith_short_12: XX7PSHWFOUFD · pith_short_16: XX7PSHWFOUFDOLM5 · pith_short_8: XX7PSHWF

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/XX7PSHWFOUFDOLM5AMTV4Q7FUS \
  | 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: bdfef91ec5750a372d9d03275e43e5a4af6f63101080c5aafcbcfab282d45383

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "989c7b382db128a86d236b018ed483aa71f91ee0dc3fef1884b8ce74e764bcda",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2009-12-28T10:25:10Z",
    "title_canon_sha256": "7f6d635e2c3e0eaef2aa50b9e1b1d987b90adb125b5d7a78a31091288a27eeb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.5146",
    "kind": "arxiv",
    "version": 1
  }
}