Pith Number

pith:HCZS42BR

pith:2014:HCZS42BR7VE4AZN7L4FS4QYJNE

not attested not anchored not stored refs pending

Big biases amongst products of two primes

Andrew Granville, David Dummit, Hershy Kisilevsky

arxiv:1411.4594 v1 · 2014-11-17 · 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{HCZS42BR7VE4AZN7L4FS4QYJNE}

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	2026-05-18T01:20:12.168090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38b32e6831fd49c065bf5f0b2e4309693042d72e3ec648fb898b5f3508888e4f

Aliases

arxiv: 1411.4594 · arxiv_version: 1411.4594v1 · doi: 10.48550/arxiv.1411.4594 · pith_short_12: HCZS42BR7VE4 · pith_short_16: HCZS42BR7VE4AZN7 · pith_short_8: HCZS42BR

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/HCZS42BR7VE4AZN7L4FS4QYJNE \
  | 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: 38b32e6831fd49c065bf5f0b2e4309693042d72e3ec648fb898b5f3508888e4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "318ea73730a5892840bf5cd7e664fad9c34e89632c8b4b94c03985cc88179640",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-11-17T19:11:16Z",
    "title_canon_sha256": "01b3bb32cdf1ac7d6fd092f5a81348f0a7350eccfe5104ebc77067b8cb6be34f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.4594",
    "kind": "arxiv",
    "version": 1
  }
}