Pith Number

pith:YMP5WMDV

pith:2010:YMP5WMDV2ENF2CQR6LW3YDRFFP

not attested not anchored not stored refs pending

Symmetries of the transfer operator for $\Gamma_0(N)$ and a character deformation of the Selberg zeta function for $\Gamma_0(4)$

Dieter Mayer, Markus Fraczek

arxiv:1011.4441 v3 · 2010-11-19 · math.NT · math-ph · math.DS · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YMP5WMDV2ENF2CQR6LW3YDRFFP}

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	2026-05-18T03:44:04.752284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c31fdb3075d11a5d0a11f2edbc0e252bdd4281f05bf0dc64aeb103244d5e88dc

Aliases

arxiv: 1011.4441 · arxiv_version: 1011.4441v3 · doi: 10.48550/arxiv.1011.4441 · pith_short_12: YMP5WMDV2ENF · pith_short_16: YMP5WMDV2ENF2CQR · pith_short_8: YMP5WMDV

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/YMP5WMDV2ENF2CQR6LW3YDRFFP \
  | 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: c31fdb3075d11a5d0a11f2edbc0e252bdd4281f05bf0dc64aeb103244d5e88dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3576f06710093aa24608de972b2100cafc6da3318df29a335e6fd4cdeb2b3b9",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-11-19T14:57:14Z",
    "title_canon_sha256": "f7d0abe64be0cf68f5308b830f6966aad0691c2b200b06e782b4b3a919e2d92b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4441",
    "kind": "arxiv",
    "version": 3
  }
}