Pith Number

pith:BESVRHYC

pith:2015:BESVRHYCAF4NC77SEAIDVBCGIU

not attested not anchored not stored refs pending

The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration

A.I. Breev, A.V. Shapovalov

arxiv:1509.08612 v1 · 2015-09-29 · 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{BESVRHYCAF4NC77SEAIDVBCGIU}

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	2026-05-18T00:53:21.086240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0925589f020178d17ff220103a844645102034ec339d7e90860bbcf9fffc2eac

Aliases

arxiv: 1509.08612 · arxiv_version: 1509.08612v1 · doi: 10.48550/arxiv.1509.08612 · pith_short_12: BESVRHYCAF4N · pith_short_16: BESVRHYCAF4NC77S · pith_short_8: BESVRHYC

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/BESVRHYCAF4NC77SEAIDVBCGIU \
  | 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: 0925589f020178d17ff220103a844645102034ec339d7e90860bbcf9fffc2eac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d946c39fad1ca21a050bd9f65e55a534afb81ccc49071092b87beb7869d6b2dd",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-09-29T07:06:50Z",
    "title_canon_sha256": "bb2b9f5a0021f2750e1206f03eede9f43157473d3b9684495a7b99c2764fda50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08612",
    "kind": "arxiv",
    "version": 1
  }
}