Pith Number

pith:4UEQDU4M

pith:2019:4UEQDU4MZJR32PZAGQQJUMWOYF

not attested not anchored not stored refs pending

Some extensions for Ramanujan's circular summation formula

Ji-Ke Ge, Qiu-Ming Luo

arxiv:1901.09820 v1 · 2019-01-24 · 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{4UEQDU4MZJR32PZAGQQJUMWOYF}

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	2026-05-17T23:55:23.749775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e50901d38cca63bd3f2034209a32cec167e252b0f63afcc159615e1c3e9f2a16

Aliases

arxiv: 1901.09820 · arxiv_version: 1901.09820v1 · doi: 10.48550/arxiv.1901.09820 · pith_short_12: 4UEQDU4MZJR3 · pith_short_16: 4UEQDU4MZJR32PZA · pith_short_8: 4UEQDU4M

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/4UEQDU4MZJR32PZAGQQJUMWOYF \
  | 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: e50901d38cca63bd3f2034209a32cec167e252b0f63afcc159615e1c3e9f2a16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c16d8ee19ae89e054516877055917f133e719f3a89e8fcaea5db4bcf36afc2f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-01-24T12:02:09Z",
    "title_canon_sha256": "1aab6496f96280b67fbe47e3724be0a80488a2cba7e1b9f28cd575f910249e85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.09820",
    "kind": "arxiv",
    "version": 1
  }
}