Pith Number

pith:RG5TME25

pith:2014:RG5TME252U6G3HWDZADU4MUOUZ

not attested not anchored not stored refs pending

Polynomial values modulo primes on average and sharpness of the larger sieve

Xuancheng Shao

arxiv:1409.7160 v1 · 2014-09-25 · 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{RG5TME252U6G3HWDZADU4MUOUZ}

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	2026-05-18T02:41:59.019374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89bb36135dd53c6d9ec3c8074e328ea66c341f64c387e623e08a13ba7cbf4729

Aliases

arxiv: 1409.7160 · arxiv_version: 1409.7160v1 · doi: 10.48550/arxiv.1409.7160 · pith_short_12: RG5TME252U6G · pith_short_16: RG5TME252U6G3HWD · pith_short_8: RG5TME25

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/RG5TME252U6G3HWDZADU4MUOUZ \
  | 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: 89bb36135dd53c6d9ec3c8074e328ea66c341f64c387e623e08a13ba7cbf4729

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89b6fb61f16e061be71e12b063df2b91c6611ee3f0e221081f1c51895249d193",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-09-25T05:33:39Z",
    "title_canon_sha256": "6818697da4cd5662982fdbf778f6fe7eb0f622a247ef1d8ac4e8cd19f95151df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.7160",
    "kind": "arxiv",
    "version": 1
  }
}