Pith Number

pith:GVLS2IIS

pith:2010:GVLS2IISV4XXNK4VQMY54GZTZS

not attested not anchored not stored refs pending

Expansion of Arbitrary Electromagnetic Fields in Terms of Vector Spherical Wave Functions

A. A. R. Neves, C. L. Cesar, M. K. Garbos, P. St. J. Russell, T. G. Euser, W. L. Moreira

arxiv:1003.2392 v3 · 2010-03-11 · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GVLS2IISV4XXNK4VQMY54GZTZS}

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	2026-05-18T00:59:28.512749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35572d2112af2f76ab958331de1b33cc8d41501d796c437523fa8c86e3f9076c

Aliases

arxiv: 1003.2392 · arxiv_version: 1003.2392v3 · doi: 10.48550/arxiv.1003.2392 · pith_short_12: GVLS2IISV4XX · pith_short_16: GVLS2IISV4XXNK4V · pith_short_8: GVLS2IIS

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/GVLS2IISV4XXNK4VQMY54GZTZS \
  | 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: 35572d2112af2f76ab958331de1b33cc8d41501d796c437523fa8c86e3f9076c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e106c7c8120ba5d764c4680bb1749df3acd9906d64849bdee6b6412e91cd766",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2010-03-11T19:18:34Z",
    "title_canon_sha256": "77666800aff47f6807434f6d64aea6c9e6939f631303bd1d3e2a65f1d09e577a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2392",
    "kind": "arxiv",
    "version": 3
  }
}