Pith Number

pith:XI32GNT2

pith:2012:XI32GNT2WVKCEKV4GHGYZ3WK4F

not attested not anchored not stored refs pending

Sumsets of reciprocals in prime fields and multilinear Kloosterman sums

J. Bourgain, M. Z. Garaev

arxiv:1211.4184 v1 · 2012-11-18 · 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{XI32GNT2WVKCEKV4GHGYZ3WK4F}

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	2026-05-18T03:40:27.726300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba37a3367ab554222abc31cd8ceecae146cde046635dc44868eb8074784a5ffb

Aliases

arxiv: 1211.4184 · arxiv_version: 1211.4184v1 · doi: 10.48550/arxiv.1211.4184 · pith_short_12: XI32GNT2WVKC · pith_short_16: XI32GNT2WVKCEKV4 · pith_short_8: XI32GNT2

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/XI32GNT2WVKCEKV4GHGYZ3WK4F \
  | 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: ba37a3367ab554222abc31cd8ceecae146cde046635dc44868eb8074784a5ffb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a6a5f9555bd7766bcb19b700716606191ff02997c57a23caffd0a587594e272",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-18T02:28:33Z",
    "title_canon_sha256": "8c3c255a442c08e786fd782c173cc3096aa94e8c5d095351a9fbefa70a4c1910"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4184",
    "kind": "arxiv",
    "version": 1
  }
}