Pith Number

pith:UKDG4PJ2

pith:2010:UKDG4PJ26EX4TKQIQULAFTFQNB

not attested not anchored not stored refs pending

Four-vector vs. four-scalar representation of the Dirac wave function

Frank Reifler, Mayeul Arminjon

arxiv:1012.2327 v2 · 2010-12-10 · gr-qc · hep-th · 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{UKDG4PJ26EX4TKQIQULAFTFQNB}

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	2026-05-18T03:56:58.266124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2866e3d3af12fc9aa08851602ccb06852e4b6c20498eb53587d0c7ce2e89db0

Aliases

arxiv: 1012.2327 · arxiv_version: 1012.2327v2 · doi: 10.48550/arxiv.1012.2327 · pith_short_12: UKDG4PJ26EX4 · pith_short_16: UKDG4PJ26EX4TKQI · pith_short_8: UKDG4PJ2

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/UKDG4PJ26EX4TKQIQULAFTFQNB \
  | 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: a2866e3d3af12fc9aa08851602ccb06852e4b6c20498eb53587d0c7ce2e89db0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdf3a27d62d741a73f6b4992401e67e2ab20c6551edb0105a6bd5e2b2d825a9b",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-12-10T17:33:16Z",
    "title_canon_sha256": "d0c40cc457852aa4aa02c950896ce7dfb9b80300612a6fa720942088d4e93dbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2327",
    "kind": "arxiv",
    "version": 2
  }
}