Pith Number

pith:LZQPCJ6S

pith:2007:LZQPCJ6STIUP3E7HSDZKSVG2LU

not attested not anchored not stored refs pending

A Generalization of a Result of Hardy and Littlewood

Ilya Vinogradov

arxiv:0709.2882 v2 · 2007-09-18 · 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{LZQPCJ6STIUP3E7HSDZKSVG2LU}

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	2026-05-18T04:09:14.474620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e60f127d29a28fd93e790f2a954da5d39b53c93362471c28231ae6e98004369

Aliases

arxiv: 0709.2882 · arxiv_version: 0709.2882v2 · doi: 10.48550/arxiv.0709.2882 · pith_short_12: LZQPCJ6STIUP · pith_short_16: LZQPCJ6STIUP3E7H · pith_short_8: LZQPCJ6S

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/LZQPCJ6STIUP3E7HSDZKSVG2LU \
  | 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: 5e60f127d29a28fd93e790f2a954da5d39b53c93362471c28231ae6e98004369

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7554854a89ac0ca23a245b4e66014321a5ba7782591b9d6ad1b8b1dcac41d84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-09-18T16:53:24Z",
    "title_canon_sha256": "c98dcd6698523c4afe9464b841e4dd0e35201fca0585abfa21eb82b257e4dfc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2882",
    "kind": "arxiv",
    "version": 2
  }
}