Pith Number

pith:DH25ERNC

pith:2007:DH25ERNC6NPL54DF57Y5XGV52Z

not attested not anchored not stored refs pending

Ruelle type L-functions versus determinants of Laplacians for torsion free abelian groups

Masato Wakayama, Nobushige Kurokawa, Yoshinori Yamasaki

arxiv:math/0702209 v2 · 2007-02-08 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DH25ERNC6NPL54DF57Y5XGV52Z}

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	2026-05-18T03:39:03.897525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19f5d245a2f35ebef065eff1db9abdd67a27d0e1b9062962f9ce5927b977b4a3

Aliases

arxiv: math/0702209 · arxiv_version: math/0702209v2 · doi: 10.48550/arxiv.math/0702209 · pith_short_12: DH25ERNC6NPL · pith_short_16: DH25ERNC6NPL54DF · pith_short_8: DH25ERNC

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/DH25ERNC6NPL54DF57Y5XGV52Z \
  | 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: 19f5d245a2f35ebef065eff1db9abdd67a27d0e1b9062962f9ce5927b977b4a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9da03a03fc2e7c506df8504f802670dbbdffd3c49109b7f53d3b3d4c0954a42e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-02-08T02:46:30Z",
    "title_canon_sha256": "11c4994c9bd2f76604b96ba340670f83901c02b07a0eb1b450787a5d661dc3f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0702209",
    "kind": "arxiv",
    "version": 2
  }
}