Pith Number

pith:GGY7LKJA

pith:2014:GGY7LKJAVJR52TXAXAE3FV6TMR

not attested not anchored not stored refs pending

A bias in Mertens' product formula

Youness Lamzouri

arxiv:1410.3777 v2 · 2014-10-14 · 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{GGY7LKJAVJR52TXAXAE3FV6TMR}

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	2026-05-18T02:27:50.924109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31b1f5a920aa63dd4ee0b809b2d7d364647fa154c21c8659016e5dc3bee11ac9

Aliases

arxiv: 1410.3777 · arxiv_version: 1410.3777v2 · doi: 10.48550/arxiv.1410.3777 · pith_short_12: GGY7LKJAVJR5 · pith_short_16: GGY7LKJAVJR52TXA · pith_short_8: GGY7LKJA

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/GGY7LKJAVJR52TXAXAE3FV6TMR \
  | 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: 31b1f5a920aa63dd4ee0b809b2d7d364647fa154c21c8659016e5dc3bee11ac9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d701b385c841c0460e5ec05c7ee34591326d93b14f41fde7a68f4a650d7fadad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-10-14T17:51:07Z",
    "title_canon_sha256": "196f098c52e02e25155837619cb50470a8bb30219e4443f8331db46b6cb5cc07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.3777",
    "kind": "arxiv",
    "version": 2
  }
}