Pith Number

pith:65C5GQAF

pith:2011:65C5GQAFQU4FVKINO2NFVVU43P

not attested not anchored not stored refs pending

Pointwise ergodic theorems beyond amenable groups

Amos Nevo, Lewis Bowen

arxiv:1103.2519 v2 · 2011-03-13 · 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{65C5GQAFQU4FVKINO2NFVVU43P}

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	2026-05-18T04:05:38.819402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f745d3400585385aa90d769a5ad69cdbc6eb21c7727af28b03d3e224834d8609

Aliases

arxiv: 1103.2519 · arxiv_version: 1103.2519v2 · doi: 10.48550/arxiv.1103.2519 · pith_short_12: 65C5GQAFQU4F · pith_short_16: 65C5GQAFQU4FVKIN · pith_short_8: 65C5GQAF

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/65C5GQAFQU4FVKINO2NFVVU43P \
  | 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: f745d3400585385aa90d769a5ad69cdbc6eb21c7727af28b03d3e224834d8609

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f9cc78a3fae135690bb882e1652c9129940e1473c490424bf1c9a11a95a021a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-03-13T14:09:40Z",
    "title_canon_sha256": "2ba4fe9838e2697fe0437134b6433f2d5bf8164e9b0790d4d8cdcc76085c1b8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2519",
    "kind": "arxiv",
    "version": 2
  }
}