Pith Number

pith:IWLWI4XX

pith:2013:IWLWI4XX7FMXNJLQAR426C5YXJ

not attested not anchored not stored refs pending

Does the Helmholtz theorem of vector decomposition apply to the wave fields of electromagnetic radiation?

A. M. Stewart

arxiv:1310.5780 v4 · 2013-10-22 · 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{IWLWI4XX7FMXNJLQAR426C5YXJ}

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	2026-05-18T02:05:24.585541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45976472f7f95976a5700479af0bb8ba4d36317aa88576f8979f8729f899d466

Aliases

arxiv: 1310.5780 · arxiv_version: 1310.5780v4 · doi: 10.48550/arxiv.1310.5780 · pith_short_12: IWLWI4XX7FMX · pith_short_16: IWLWI4XX7FMXNJLQ · pith_short_8: IWLWI4XX

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/IWLWI4XX7FMXNJLQAR426C5YXJ \
  | 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: 45976472f7f95976a5700479af0bb8ba4d36317aa88576f8979f8729f899d466

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a8dfd55e034784c89803c972d60bce3877bc0d4b75cb544398f728b129fb86b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2013-10-22T02:22:29Z",
    "title_canon_sha256": "9e1108bf2933de38e5145f587cdac97ae8fff0a1c7ebf419848dde4d541b5cd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.5780",
    "kind": "arxiv",
    "version": 4
  }
}