Pith Number

pith:PP4M3YOW

pith:2010:PP4M3YOWRDUPQ6WH7LOYEXSLDW

not attested not anchored not stored refs pending

Pointwise convergence for cubic and polynomial ergodic averages of non-commuting transformations

Nikos Frantzikinakis, Qing Chu

arxiv:1006.5239 v2 · 2010-06-27 · 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{PP4M3YOWRDUPQ6WH7LOYEXSLDW}

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	2026-05-18T04:29:53.633555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bf8cde1d688e8f87ac7fadd825e4b1da954bcf79582bda3032fdcfe6e9a8339

Aliases

arxiv: 1006.5239 · arxiv_version: 1006.5239v2 · doi: 10.48550/arxiv.1006.5239 · pith_short_12: PP4M3YOWRDUP · pith_short_16: PP4M3YOWRDUPQ6WH · pith_short_8: PP4M3YOW

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/PP4M3YOWRDUPQ6WH7LOYEXSLDW \
  | 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: 7bf8cde1d688e8f87ac7fadd825e4b1da954bcf79582bda3032fdcfe6e9a8339

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cef3de1b4408f4d61e4b29af03d89d2b152ef10cc7bd7bb8bc87dfcda3068485",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-06-27T22:03:39Z",
    "title_canon_sha256": "76d3189812218242ddb5ccf0dad46aa33b7c7d79dcd30cc4259dfc03a8e24aa7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.5239",
    "kind": "arxiv",
    "version": 2
  }
}