Pith Number

pith:5ACCTXYP

pith:2010:5ACCTXYPCCYLIN5OAQQW6QDO6Q

not attested not anchored not stored refs pending

On the functional determinant of a special operator with a zero mode in cosmology

A.O.Barvinsky, A.Yu.Kamenshchik

arxiv:1012.1571 v2 · 2010-12-07 · hep-th · gr-qc · 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{5ACCTXYPCCYLIN5OAQQW6QDO6Q}

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	2026-05-18T04:12:12.020970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e80429df0f10b0b437ae04216f406ef4384f8373123c54a4e3e5cf31e33ed2fd

Aliases

arxiv: 1012.1571 · arxiv_version: 1012.1571v2 · doi: 10.48550/arxiv.1012.1571 · pith_short_12: 5ACCTXYPCCYL · pith_short_16: 5ACCTXYPCCYLIN5O · pith_short_8: 5ACCTXYP

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/5ACCTXYPCCYLIN5OAQQW6QDO6Q \
  | 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: e80429df0f10b0b437ae04216f406ef4384f8373123c54a4e3e5cf31e33ed2fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5d52c9257b7ed213cb3b1811703fb5ed297025118628645e7b5c844b1f3cd3b",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2010-12-07T18:17:58Z",
    "title_canon_sha256": "0e373219451b604fe54aa7e28545fae746cf4be2deef61f3e15ee8a9196990ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1571",
    "kind": "arxiv",
    "version": 2
  }
}