Pith Number

pith:N2EU2FEV

pith:2012:N2EU2FEVCSHBSK3MG2KQVNAVUX

not attested not anchored not stored refs pending

On Congruences with Products of Variables from Short Intervals and Applications

Igor Shparlinski, Jean Bourgain, Moubariz Garaev, Sergei Konyagin

arxiv:1203.0017 v1 · 2012-02-29 · 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{N2EU2FEVCSHBSK3MG2KQVNAVUX}

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	2026-05-18T04:01:03.427071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e894d1495148e192b6c36950ab415a5d9beadc8e9011bb9462e6aa02dab1d38

Aliases

arxiv: 1203.0017 · arxiv_version: 1203.0017v1 · doi: 10.48550/arxiv.1203.0017 · pith_short_12: N2EU2FEVCSHB · pith_short_16: N2EU2FEVCSHBSK3M · pith_short_8: N2EU2FEV

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/N2EU2FEVCSHBSK3MG2KQVNAVUX \
  | 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: 6e894d1495148e192b6c36950ab415a5d9beadc8e9011bb9462e6aa02dab1d38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "048d6a7f8686d8b115a4b8e33ef755596281b67bbe66a89e794abbff7b9f375d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-02-29T21:09:46Z",
    "title_canon_sha256": "556326a78c64892f15bcb7fd57b1a313003d3054f52284fe349c74bc7712c43d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0017",
    "kind": "arxiv",
    "version": 1
  }
}