Pith Number

pith:VC2IT5IN

pith:2017:VC2IT5INYMWPXO4V7C2QXLJQSQ

not attested not anchored not stored refs pending

Bombieri-Vinogradov for multiplicative functions, and beyond the $x^{1/2}$-barrier

Andrew Granville, Xuancheng Shao

arxiv:1703.06865 v2 · 2017-03-20 · 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{VC2IT5INYMWPXO4V7C2QXLJQSQ}

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	2026-05-17T23:48:12.074384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8b489f50dc32cfbbb95f8b50bad3094096f7917da4e0efef492bbcd05b9d8b1

Aliases

arxiv: 1703.06865 · arxiv_version: 1703.06865v2 · doi: 10.48550/arxiv.1703.06865 · pith_short_12: VC2IT5INYMWP · pith_short_16: VC2IT5INYMWPXO4V · pith_short_8: VC2IT5IN

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/VC2IT5INYMWPXO4V7C2QXLJQSQ \
  | 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: a8b489f50dc32cfbbb95f8b50bad3094096f7917da4e0efef492bbcd05b9d8b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65c99a27460147deb20e9eb0c791cf27c096855495adc6caef2c5863355e378a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-03-20T17:41:11Z",
    "title_canon_sha256": "b046dad36cda5e70eefbcce1fc8a892ea3e16ccad918accd34534e917b0e2517"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.06865",
    "kind": "arxiv",
    "version": 2
  }
}