Pith Number

pith:Z3NAGCDO

pith:2010:Z3NAGCDOOR3CSTGCIJZHHCR6HJ

not attested not anchored not stored refs pending

Barnes multiple zeta-functions, Ramanujan's formula, and relevant series involving hyperbolic functions

Hirofumi Tsumura, Kohji Matsumoto, Yasushi Komori

arxiv:1006.3336 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{Z3NAGCDOOR3CSTGCIJZHHCR6HJ}

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	2026-05-18T02:43:59.567279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceda03086e7476294cc24272738a3e3a6ceca56c3a379de54e28506fed8dfdec

Aliases

arxiv: 1006.3336 · arxiv_version: 1006.3336v1 · doi: 10.48550/arxiv.1006.3336 · pith_short_12: Z3NAGCDOOR3C · pith_short_16: Z3NAGCDOOR3CSTGC · pith_short_8: Z3NAGCDO

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/Z3NAGCDOOR3CSTGCIJZHHCR6HJ \
  | 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: ceda03086e7476294cc24272738a3e3a6ceca56c3a379de54e28506fed8dfdec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b8047b05a25f12876166c4d0b5abbc0a4694606f96f5a8c2d882f75d2feb0ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-06-16T22:42:33Z",
    "title_canon_sha256": "00acb4b8b49b7dd72e90ae89c55dcb8570a80e7a5a36aa92c14c4ea4b1783278"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3336",
    "kind": "arxiv",
    "version": 1
  }
}