Pith Number

pith:YXJL7PYT

pith:2010:YXJL7PYTOLSJBQTD2GVAWLCWK3

not attested not anchored not stored refs pending

Sums and Products with Smooth Numbers

David Covert, William D. Banks

arxiv:1010.3322 v1 · 2010-10-16 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YXJL7PYTOLSJBQTD2GVAWLCWK3}

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	2026-05-18T04:39:09.465922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5d2bfbf1372e490c263d1aa0b2c5656f7c91bde64984fa0bf329ac17fa4dbdc

Aliases

arxiv: 1010.3322 · arxiv_version: 1010.3322v1 · doi: 10.48550/arxiv.1010.3322 · pith_short_12: YXJL7PYTOLSJ · pith_short_16: YXJL7PYTOLSJBQTD · pith_short_8: YXJL7PYT

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/YXJL7PYTOLSJBQTD2GVAWLCWK3 \
  | 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: c5d2bfbf1372e490c263d1aa0b2c5656f7c91bde64984fa0bf329ac17fa4dbdc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77c0072cce4d2bc464b43d1cc0825471a6ee06b1c0897fc96649ae5528c88e30",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-10-16T05:38:39Z",
    "title_canon_sha256": "beed7de99193d6e33375897eef0422682d79aa535600480f0dd8aeee1455c334"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3322",
    "kind": "arxiv",
    "version": 1
  }
}