Pith Number

pith:ZWQ4SA4L

pith:2019:ZWQ4SA4LZOYSSH3C6RWQEJTM6S

not attested not anchored not stored refs pending

Simple proof of Bourgain bilinear ergodic theorem and its extension to polynomials and polynomials in primes

E. H. El Abdalaoui

arxiv:1908.02281 v1 · 2019-08-05 · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZWQ4SA4LZOYSSH3C6RWQEJTM6S}

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	2026-07-04T23:52:07.089960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cda1c9038bcbb1291f62f46d02266cf4b6df763dfa8bf671d2900fb48609b49d

Aliases

arxiv: 1908.02281 · arxiv_version: 1908.02281v1 · doi: 10.48550/arxiv.1908.02281 · pith_short_12: ZWQ4SA4LZOYS · pith_short_16: ZWQ4SA4LZOYSSH3C · pith_short_8: ZWQ4SA4L

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/ZWQ4SA4LZOYSSH3C6RWQEJTM6S \
  | 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: cda1c9038bcbb1291f62f46d02266cf4b6df763dfa8bf671d2900fb48609b49d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c49afb166f37f0788371b465354762cb6061ff12fc32d4341e71610ae42edac5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-08-05T18:11:44Z",
    "title_canon_sha256": "e2e29f1b0389d22940540dfe2ad946fcc0875309cb544281202bc2d3c91860e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02281",
    "kind": "arxiv",
    "version": 1
  }
}