Pith Number

pith:7XQ6RUXF

pith:2019:7XQ6RUXFPOFPEMONLJIPSGDPXX

not attested not anchored not stored refs pending

Twisted Localized Solutions of the Dirac Equation: Hopfion-like States of Relativistic Electrons

Iwo Bialynicki-Birula, Zofia Bialynicka-Birula

arxiv:1901.01532 v2 · 2019-01-06 · 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{7XQ6RUXFPOFPEMONLJIPSGDPXX}

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	2026-05-17T23:40:33.779601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde1e8d2e57b8af231cd5a50f9186fbdd22a9405ecaa932f001553bd839db0b1

Aliases

arxiv: 1901.01532 · arxiv_version: 1901.01532v2 · doi: 10.48550/arxiv.1901.01532 · pith_short_12: 7XQ6RUXFPOFP · pith_short_16: 7XQ6RUXFPOFPEMON · pith_short_8: 7XQ6RUXF

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/7XQ6RUXFPOFPEMONLJIPSGDPXX \
  | 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: fde1e8d2e57b8af231cd5a50f9186fbdd22a9405ecaa932f001553bd839db0b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2264bdc5eeec2a3301ff5fe389ad6b75cabd600746349f4a54df5d42bee499ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2019-01-06T12:03:23Z",
    "title_canon_sha256": "59d12e1c029f2e03482d0c55bdb2dc5ffe7eb1e4c020f544f21281e3a6b4e1e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.01532",
    "kind": "arxiv",
    "version": 2
  }
}