Pith Number

pith:KTDE7XKN

pith:2012:KTDE7XKN7ESI7CGBCKPMJF6E77

not attested not anchored not stored refs pending

Comment on the sums $S(n)=\sum\limits_{k=-\infty}^\infty \frac{1}{(4k+1)^n}$

Z. K. Silagadze

arxiv:1207.2055 v1 · 2012-07-09 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KTDE7XKN7ESI7CGBCKPMJF6E77}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T03:45:55.061492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54c64fdd4df9248f88c1129ec497c4ffde9992c5db93bc138d81f5db4b1edf9a

Aliases

arxiv: 1207.2055 · arxiv_version: 1207.2055v1 · doi: 10.48550/arxiv.1207.2055 · pith_short_12: KTDE7XKN7ESI · pith_short_16: KTDE7XKN7ESI7CGB · pith_short_8: KTDE7XKN

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/KTDE7XKN7ESI7CGBCKPMJF6E77 \
  | 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: 54c64fdd4df9248f88c1129ec497c4ffde9992c5db93bc138d81f5db4b1edf9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed01228b7785808d2275abce0444f80a272c8c4cd46f2e33a49213007c0bd7a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-07-09T14:15:33Z",
    "title_canon_sha256": "e006d9ec3bdd8146a3d2a785ffaf347fd407de84e882c484dd8d2227a68bf6f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2055",
    "kind": "arxiv",
    "version": 1
  }
}