Pith Number

pith:TDNCB22I

pith:2019:TDNCB22I5HTDXJZH2ERNB3XXXL

not attested not anchored not stored refs pending

A Comment on the Sums $\sum_{n \in \mathbb{Z}} \frac{(-1)^{nk}}{(an+1)^k}$

Vivek Kaushik

arxiv:1903.03561 v1 · 2019-03-05 · 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{TDNCB22I5HTDXJZH2ERNB3XXXL}

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	2026-05-17T23:51:45.168219Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98da20eb48e9e63ba727d122d0eef7baf8e6a0211f68c82b4361de09adec738d

Aliases

arxiv: 1903.03561 · arxiv_version: 1903.03561v1 · doi: 10.48550/arxiv.1903.03561 · pith_short_12: TDNCB22I5HTD · pith_short_16: TDNCB22I5HTDXJZH · pith_short_8: TDNCB22I

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/TDNCB22I5HTDXJZH2ERNB3XXXL \
  | 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: 98da20eb48e9e63ba727d122d0eef7baf8e6a0211f68c82b4361de09adec738d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f58d79a17a7dba704c6e88a16a0f2846f1f3f67637e02c1baf71673d3d75554",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-03-05T07:44:06Z",
    "title_canon_sha256": "a615cbf03e3e32bd0f7f86cc84549903d044746d0ce9e41ff6f67a1f8afb88a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.03561",
    "kind": "arxiv",
    "version": 1
  }
}