Pith Number

pith:LP2AKZIG

pith:2013:LP2AKZIGYHAY6SXEUCK7JGKOFB

not attested not anchored not stored refs pending

Sums of products of fractional parts

Jeffrey D. Vaaler, Thai Hoang Le

arxiv:1309.1506 v1 · 2013-09-05 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LP2AKZIGYHAY6SXEUCK7JGKOFB}

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	2026-05-18T03:13:59.299165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bf4056506c1c18f4ae4a095f4994e286363cce2ed63884ea842fd7f52a91337

Aliases

arxiv: 1309.1506 · arxiv_version: 1309.1506v1 · doi: 10.48550/arxiv.1309.1506 · pith_short_12: LP2AKZIGYHAY · pith_short_16: LP2AKZIGYHAY6SXE · pith_short_8: LP2AKZIG

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/LP2AKZIGYHAY6SXEUCK7JGKOFB \
  | 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: 5bf4056506c1c18f4ae4a095f4994e286363cce2ed63884ea842fd7f52a91337

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a693e7a544fcd1dc0ddb651c65020be90849dd911f2691c9f6d4317af1aa02a8",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-05T22:52:52Z",
    "title_canon_sha256": "7e99e9ce169713744d694f8e36133fe5e5bc0e25b755819fbd5c1c93642e3d46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1506",
    "kind": "arxiv",
    "version": 1
  }
}