Pith Number

pith:PW272ZLR

pith:2008:PW272ZLR7X2MLBGYAVFPKHDHF5

not attested not anchored not stored refs pending

Selberg's zeta functions for congruence subgroups of modular groups in SL(2,R) and SL(2,C)

Yasufumi Hashimoto

arxiv:0806.4829 v3 · 2008-06-30 · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PW272ZLR7X2MLBGYAVFPKHDHF5}

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	2026-05-18T02:27:49.960774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7db5fd6571fdf4c584d8054af51c672f50c87b79b1924516f7d296f2f0d432b0

Aliases

arxiv: 0806.4829 · arxiv_version: 0806.4829v3 · doi: 10.48550/arxiv.0806.4829 · pith_short_12: PW272ZLR7X2M · pith_short_16: PW272ZLR7X2MLBGY · pith_short_8: PW272ZLR

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/PW272ZLR7X2MLBGYAVFPKHDHF5 \
  | 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: 7db5fd6571fdf4c584d8054af51c672f50c87b79b1924516f7d296f2f0d432b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c16e2b606f4d12728af721facf8c80b6d9a51ec26f60de34258c4add3d3d81c",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-06-30T08:47:04Z",
    "title_canon_sha256": "9a95c38d5f6f644f6dfed30cbcfbb2636b82f8e9646e106211f22deac5fbfe84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.4829",
    "kind": "arxiv",
    "version": 3
  }
}