Pith Number

pith:KG4WR4YY

pith:2012:KG4WR4YYOPLUSISITP23XPZH5N

not attested not anchored not stored refs pending

Evaluation of the convolution sums $\sum_{l+15m=n} \sigma(l) \sigma(m)$ and $\sum_{3l+5m=n} \sigma(l) \sigma(m)$ and some applications

B. Ramakrishnan, Brundaban Sahu

arxiv:1207.5107 v2 · 2012-07-21 · 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{KG4WR4YYOPLUSISITP23XPZH5N}

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	2026-05-18T03:42:44.089156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51b968f31873d74922489bf5bbbf27eb7c5a1ba4ea844955083f053d7021e619

Aliases

arxiv: 1207.5107 · arxiv_version: 1207.5107v2 · doi: 10.48550/arxiv.1207.5107 · pith_short_12: KG4WR4YYOPLU · pith_short_16: KG4WR4YYOPLUSISI · pith_short_8: KG4WR4YY

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/KG4WR4YYOPLUSISITP23XPZH5N \
  | 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: 51b968f31873d74922489bf5bbbf27eb7c5a1ba4ea844955083f053d7021e619

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5630f1955b26ac90cceefcffad80e6973ae58f38f1861efeff644f7bcd1176c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-07-21T07:11:53Z",
    "title_canon_sha256": "30640f459a676dfd6c18c9876fe12d8e2d69a9e1b95e90401d25178ce9392f71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5107",
    "kind": "arxiv",
    "version": 2
  }
}