Pith Number

pith:K4AL5EZD

pith:2011:K4AL5EZD5UM3N5ETIYKZKFVO25

not attested not anchored not stored refs pending

Geometric Momentum: the Proper Momentum for a Free Particle on a Two-dimensional Sphere

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

arxiv:1109.5223 v1 · 2011-09-24 · quant-ph · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K4AL5EZD5UM3N5ETIYKZKFVO25}

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	2026-05-18T02:00:25.673225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5700be9323ed19b6f49346159516aed740aa0f1deea99856f7255df1c5426bd3

Aliases

arxiv: 1109.5223 · arxiv_version: 1109.5223v1 · doi: 10.48550/arxiv.1109.5223 · pith_short_12: K4AL5EZD5UM3 · pith_short_16: K4AL5EZD5UM3N5ET · pith_short_8: K4AL5EZD

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/K4AL5EZD5UM3N5ETIYKZKFVO25 \
  | 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: 5700be9323ed19b6f49346159516aed740aa0f1deea99856f7255df1c5426bd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e36e47ff85722a60bdecbb1f5d2dfecd7f8ccf88776fe09a4050abf605a23e9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-09-24T02:14:25Z",
    "title_canon_sha256": "09abc5be528d84b94a819b9097bd1af194c6e79589c190801fd71d149cc1ea57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5223",
    "kind": "arxiv",
    "version": 1
  }
}