Pith Number

pith:QX3UZOCK

pith:2010:QX3UZOCKY2434RPJ3SULA2QK43

not attested not anchored not stored refs pending

Smooth numbers in short intervals

K. Soundararajan

arxiv:1009.1591 v1 · 2010-09-08 · 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{QX3UZOCKY2434RPJ3SULA2QK43}

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	2026-05-18T04:41:14.443573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85f74cb84ac6b9be45e9dca8b06a0ae6c5b5c52e0d13fa6994551b9f127ad704

Aliases

arxiv: 1009.1591 · arxiv_version: 1009.1591v1 · doi: 10.48550/arxiv.1009.1591 · pith_short_12: QX3UZOCKY243 · pith_short_16: QX3UZOCKY2434RPJ · pith_short_8: QX3UZOCK

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/QX3UZOCKY2434RPJ3SULA2QK43 \
  | 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: 85f74cb84ac6b9be45e9dca8b06a0ae6c5b5c52e0d13fa6994551b9f127ad704

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c0def510dadc92846b69945e29ffeafad4ef01a9cd05895ab302407850c4c33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-09-08T17:19:59Z",
    "title_canon_sha256": "94524fe250b76c19f283c3e9fcdd18569974f1f08664f54c87c1c6da8170b2f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1591",
    "kind": "arxiv",
    "version": 1
  }
}