Pith Number

pith:IJL4K6R2

pith:2011:IJL4K6R2FDTTE2MAVYQGO5MPLT

not attested not anchored not stored refs pending

An L^1 ergodic theorem with values in a nonpositively curved space via a canonical barycenter map

Andr\'es Navas

arxiv:1104.5188 v3 · 2011-04-27 · math.DS · math.GR · 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{IJL4K6R2FDTTE2MAVYQGO5MPLT}

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	2026-05-18T04:05:59.295872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4257c57a3a28e7326980ae2067758f5cc46dc44d92823d40b00803ed2f2e3169

Aliases

arxiv: 1104.5188 · arxiv_version: 1104.5188v3 · doi: 10.48550/arxiv.1104.5188 · pith_short_12: IJL4K6R2FDTT · pith_short_16: IJL4K6R2FDTTE2MA · pith_short_8: IJL4K6R2

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/IJL4K6R2FDTTE2MAVYQGO5MPLT \
  | 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: 4257c57a3a28e7326980ae2067758f5cc46dc44d92823d40b00803ed2f2e3169

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4331faf29ab7e1993e0337027ff4ac42c5cae6d2dddf0b530c0fed07fe7bb339",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-04-27T16:56:04Z",
    "title_canon_sha256": "43c4df210e552afdc7929ec6a90462794cdd9f9ee3bb9fc180a567a996625b2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.5188",
    "kind": "arxiv",
    "version": 3
  }
}