Pith Number

pith:HZQB2AUZ

pith:2015:HZQB2AUZOJY54PN6B6F3LQ6KZU

not attested not anchored not stored refs pending

General divisor functions in arithmetic progressions to large moduli

Boqing Xue, Fei Wei, Yitang Zhang

arxiv:1512.01470 v1 · 2015-12-04 · 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{HZQB2AUZOJY54PN6B6F3LQ6KZU}

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	2026-05-18T01:08:12.594857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e601d02997271de3dbe0f8bb5c3cacd2d6487c91a46dc3258bdae10226369ae

Aliases

arxiv: 1512.01470 · arxiv_version: 1512.01470v1 · doi: 10.48550/arxiv.1512.01470 · pith_short_12: HZQB2AUZOJY5 · pith_short_16: HZQB2AUZOJY54PN6 · pith_short_8: HZQB2AUZ

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/HZQB2AUZOJY54PN6B6F3LQ6KZU \
  | 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: 3e601d02997271de3dbe0f8bb5c3cacd2d6487c91a46dc3258bdae10226369ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3803e1ff57ef039bd6523ff6868320f0dc4b9f4498088670da6791c33562c392",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-04T16:30:11Z",
    "title_canon_sha256": "b420698654660fdd8bb15857c41f3eae8cf3da4bf36cb9c003a026e9fa5da9d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01470",
    "kind": "arxiv",
    "version": 1
  }
}