Pith Number

pith:TKIXSAQC

pith:2012:TKIXSAQCPWAT45K4DD3RXOOFT3

not attested not anchored not stored refs pending

A New Formula for The Values of Dirichlet Beta Function at Odd Positive Integers Based on The WZ Method

Yijun Chen

arxiv:1211.3149 v1 · 2012-11-13 · math.CO · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TKIXSAQCPWAT45K4DD3RXOOFT3}

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	2026-05-18T03:40:50.765295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a917902027d813e755c18f71bb9c59ef2ad0630cb5b7f1a15bc150d83c5dc9f

Aliases

arxiv: 1211.3149 · arxiv_version: 1211.3149v1 · doi: 10.48550/arxiv.1211.3149 · pith_short_12: TKIXSAQCPWAT · pith_short_16: TKIXSAQCPWAT45K4 · pith_short_8: TKIXSAQC

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/TKIXSAQCPWAT45K4DD3RXOOFT3 \
  | 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: 9a917902027d813e755c18f71bb9c59ef2ad0630cb5b7f1a15bc150d83c5dc9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cec0412160d8bc7c0bfbfccb777bf0a54693edf3f5717c4d9e810d97a07e23fd",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-13T22:06:56Z",
    "title_canon_sha256": "4a5ff78eeb8d582555b9ebbf1f681bb578ef098977f14db8f58739261bb2a028"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3149",
    "kind": "arxiv",
    "version": 1
  }
}