Pith Number

pith:BYWJVQ5U

pith:2025:BYWJVQ5UJCT3HL46D7QCDZVXCV

not attested not anchored not stored refs pending

Madelung Structure of the Dirac Equation

Luca Fabbri

arxiv:2505.05861 v1 · 2025-05-09 · 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{BYWJVQ5UJCT3HL46D7QCDZVXCV}

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.

Cited by

2 papers in Pith

The Schrodinger Equation as a Gauge Theory

Receipt and verification

First computed	2026-07-05T11:00:48.932288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e2c9ac3b448a7b3af9e1fe021e6b71547e3b35bc19ab397140d15768103bc90

Aliases

arxiv: 2505.05861 · arxiv_version: 2505.05861v1 · doi: 10.48550/arxiv.2505.05861 · pith_short_12: BYWJVQ5UJCT3 · pith_short_16: BYWJVQ5UJCT3HL46 · pith_short_8: BYWJVQ5U

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/BYWJVQ5UJCT3HL46D7QCDZVXCV \
  | 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: 0e2c9ac3b448a7b3af9e1fe021e6b71547e3b35bc19ab397140d15768103bc90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "298edf75ce43efe940513363e329ec287cfea557f613c5ce96fbaaee63368d86",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-05-09T07:54:18Z",
    "title_canon_sha256": "ed7eb0d46ba9bd5e4c0ba6e1612bda239ff165df872bf9544ce2db19efb48854"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.05861",
    "kind": "arxiv",
    "version": 1
  }
}