Pith Number

pith:WIPWAUZM

pith:2013:WIPWAUZMU45Q6EIGY54EPVX6XI

not attested not anchored not stored refs pending

On sums of generalized Ramanujan sums

Yusuke Fujisawa

arxiv:1303.6070 v2 · 2013-03-25 · 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{WIPWAUZMU45Q6EIGY54EPVX6XI}

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	2026-05-18T03:10:58.107698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b21f60532ca73b0f1106c77847d6feba374699b99c91b8692d77c04fa0083a40

Aliases

arxiv: 1303.6070 · arxiv_version: 1303.6070v2 · doi: 10.48550/arxiv.1303.6070 · pith_short_12: WIPWAUZMU45Q · pith_short_16: WIPWAUZMU45Q6EIG · pith_short_8: WIPWAUZM

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/WIPWAUZMU45Q6EIGY54EPVX6XI \
  | 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: b21f60532ca73b0f1106c77847d6feba374699b99c91b8692d77c04fa0083a40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fafac04280f8394cf551d6cf4878b001769a66f4bb52905955719e09359b4a0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-03-25T10:04:39Z",
    "title_canon_sha256": "6638b7036241e097cc6b00df2b5b87cb9f6800d71b638e911f221e0875a3a2d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.6070",
    "kind": "arxiv",
    "version": 2
  }
}