Pith Number

pith:SXO2XMBT

pith:2019:SXO2XMBTPPADNDK73GFVOLUW3I

not attested not anchored not stored refs pending

Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences

Jes\'us Guillera

arxiv:1908.05123 v1 · 2019-08-14 · 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{SXO2XMBTPPADNDK73GFVOLUW3I}

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	2026-07-04T23:56:36.499551Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95ddabb0337bc0368d5fd98b572e96da1664fb1e42ea2ff1d7968da53a9eab35

Aliases

arxiv: 1908.05123 · arxiv_version: 1908.05123v1 · doi: 10.48550/arxiv.1908.05123 · pith_short_12: SXO2XMBTPPAD · pith_short_16: SXO2XMBTPPADNDK7 · pith_short_8: SXO2XMBT

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/SXO2XMBTPPADNDK73GFVOLUW3I \
  | 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: 95ddabb0337bc0368d5fd98b572e96da1664fb1e42ea2ff1d7968da53a9eab35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02c04fc15ca4ff012a1bb6c91aea65d1bbd5d60e05702632a44a6658cca0efbd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-08-14T13:44:01Z",
    "title_canon_sha256": "88b3bbfe92a68aa6d2d99deb688e2bae37b404ef294dc183663415ddde6a3c5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.05123",
    "kind": "arxiv",
    "version": 1
  }
}