Pith Number

pith:PLPW7623

pith:2009:PLPW7623PXX32B4JFAZFORNMJ7

not attested not anchored not stored refs pending

The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker Universe

Felix Finster, Moritz Reintjes

arxiv:0901.0602 v4 · 2009-01-06 · math-ph · gr-qc · 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{PLPW7623PXX32B4JFAZFORNMJ7}

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	2026-05-18T03:34:25.902890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7adf6ffb5b7defbd078928325745ac4ffa5d17692d6f42a1cea8240c11200343

Aliases

arxiv: 0901.0602 · arxiv_version: 0901.0602v4 · doi: 10.48550/arxiv.0901.0602 · pith_short_12: PLPW7623PXX3 · pith_short_16: PLPW7623PXX32B4J · pith_short_8: PLPW7623

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/PLPW7623PXX32B4JFAZFORNMJ7 \
  | 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: 7adf6ffb5b7defbd078928325745ac4ffa5d17692d6f42a1cea8240c11200343

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2dddbbf749fe931b487bd052eb685a9b0ee5c956c78e35de9ff760b3f9e019e",
    "cross_cats_sorted": [
      "gr-qc",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-01-06T08:00:46Z",
    "title_canon_sha256": "4cb6e6cd268015d7248a61c39953b8b331b94ff30b729988d9466bdd327a7993"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.0602",
    "kind": "arxiv",
    "version": 4
  }
}