Pith Number

pith:5KBGD4X5

pith:2009:5KBGD4X5YNT562DGHJICA77NMF

not attested not anchored not stored refs pending

Ergodic averages of commuting transformations with distinct degree polynomial iterates

Bernard Host, Nikos Frantzikinakis, Qing Chu

arxiv:0912.2641 v4 · 2009-12-14 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5KBGD4X5YNT562DGHJICA77NMF}

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	2026-05-18T01:26:39.955554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea8261f2fdc367df68663a50207fed6141eda4c8eda1ae70d2b61827fdbed2b7

Aliases

arxiv: 0912.2641 · arxiv_version: 0912.2641v4 · doi: 10.48550/arxiv.0912.2641 · pith_short_12: 5KBGD4X5YNT5 · pith_short_16: 5KBGD4X5YNT562DG · pith_short_8: 5KBGD4X5

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/5KBGD4X5YNT562DGHJICA77NMF \
  | 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: ea8261f2fdc367df68663a50207fed6141eda4c8eda1ae70d2b61827fdbed2b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd92800c8163b54396b449889d7da977c2e7ab7e821cb38404887889979039d7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-12-14T13:11:21Z",
    "title_canon_sha256": "2db71379c58f500c74c68521c60ef136b658d1330b4f70c872bb63946dedd482"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2641",
    "kind": "arxiv",
    "version": 4
  }
}