Pith Number

pith:5CPM2GTL

pith:2016:5CPM2GTLZDQVY6UWTIYP2CNFMO

not attested not anchored not stored refs pending

A cubic nonconventional ergodic average with multiplicative or Mangoldt weights

el Houcein el Abdalaoui, Xiangdong Ye

arxiv:1606.05630 v2 · 2016-06-17 · math.DS · math.CO · math.CV · 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{5CPM2GTLZDQVY6UWTIYP2CNFMO}

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	2026-05-18T01:00:12.263096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e89ecd1a6bc8e15c7a969a30fd09a56394f7583847f4a2ee6440e02994bfadb3

Aliases

arxiv: 1606.05630 · arxiv_version: 1606.05630v2 · doi: 10.48550/arxiv.1606.05630 · pith_short_12: 5CPM2GTLZDQV · pith_short_16: 5CPM2GTLZDQVY6UW · pith_short_8: 5CPM2GTL

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/5CPM2GTLZDQVY6UWTIYP2CNFMO \
  | 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: e89ecd1a6bc8e15c7a969a30fd09a56394f7583847f4a2ee6440e02994bfadb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6ab17308b67cebf16369e741caae849a64116c1da45dfb1016bfc66ea3b2fda",
    "cross_cats_sorted": [
      "math.CO",
      "math.CV",
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-06-17T19:25:50Z",
    "title_canon_sha256": "52d34decf6070097e5beaea54a362f3c0e468553a54d2256415985ab6e04e937"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.05630",
    "kind": "arxiv",
    "version": 2
  }
}