Pith Number

pith:ZM37NRT4

pith:2010:ZM37NRT4YO2VISP2EY6ZGKH3IH

not attested not anchored not stored refs pending

Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and $q$-zeta functions

Hirofumi Tsumura, Kohji Matsumoto, Yasushi Komori

arxiv:1006.3339 v1 · 2010-06-16 · 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{ZM37NRT4YO2VISP2EY6ZGKH3IH}

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	2026-05-18T01:16:07.749956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb37f6c67cc3b55449fa263d9328fb41e93e847725a6d65c06e1633c4360ba1c

Aliases

arxiv: 1006.3339 · arxiv_version: 1006.3339v1 · doi: 10.48550/arxiv.1006.3339 · pith_short_12: ZM37NRT4YO2V · pith_short_16: ZM37NRT4YO2VISP2 · pith_short_8: ZM37NRT4

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/ZM37NRT4YO2VISP2EY6ZGKH3IH \
  | 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: cb37f6c67cc3b55449fa263d9328fb41e93e847725a6d65c06e1633c4360ba1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32bb27bda6fcaae0c2b886280d03137a7f873112a2e1602851ad37a72c58c810",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-06-16T22:55:00Z",
    "title_canon_sha256": "159758f1bb594d59f39049e27faf155d6a9a9cfa299ae1394bbde2c7a016405c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3339",
    "kind": "arxiv",
    "version": 1
  }
}