Pith Number

pith:NYO327GX

pith:2017:NYO327GXD7XJI4VVQ72SOOGA5Q

not attested not anchored not stored refs pending

On the homogeneous ergodic bilinear averages with M\"{o}bius and liouville weights

el Houcein el Abdalaoui

arxiv:1706.07280 v4 · 2017-06-15 · math.CA · math.FA · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NYO327GXD7XJI4VVQ72SOOGA5Q}

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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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-05T00:13:35.061571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e1dbd7cd71fee9472b587f52738c0ec0293ab0a4b2bfcac2d42eb872888f350

Aliases

arxiv: 1706.07280 · arxiv_version: 1706.07280v4 · doi: 10.48550/arxiv.1706.07280 · pith_short_12: NYO327GXD7XJ · pith_short_16: NYO327GXD7XJI4VV · pith_short_8: NYO327GX

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/NYO327GXD7XJI4VVQ72SOOGA5Q \
  | 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: 6e1dbd7cd71fee9472b587f52738c0ec0293ab0a4b2bfcac2d42eb872888f350

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2ae62369b9c62dffddcc9ade180a222610c1ba2b14f858b90b74582c1e9b652",
    "cross_cats_sorted": [
      "math.FA",
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-06-15T20:56:34Z",
    "title_canon_sha256": "e999ab50f5a445c04d081d7ced141512d69632f12bb848837a2d6a1beabaf505"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.07280",
    "kind": "arxiv",
    "version": 4
  }
}