Pith Number

pith:T3TZ6GEG

pith:2005:T3TZ6GEGEEC6ZRNRITYGSOOPHI

not attested not anchored not stored refs pending

Noncommutative maximal ergodic theorems

Marius Junge, Quanhua Xu

arxiv:math/0505308 v2 · 2005-05-14 · math.OA · math.DS · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T3TZ6GEGEEC6ZRNRITYGSOOPHI}

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	2026-07-04T14:50:13.549399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ee79f18862105ecc5b144f06939cf3a168f33143db0b7249dc8d3f1cdfc4cc7

Aliases

arxiv: math/0505308 · arxiv_version: math/0505308v2 · doi: 10.48550/arxiv.math/0505308 · pith_short_12: T3TZ6GEGEEC6 · pith_short_16: T3TZ6GEGEEC6ZRNR · pith_short_8: T3TZ6GEG

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/T3TZ6GEGEEC6ZRNRITYGSOOPHI \
  | 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: 9ee79f18862105ecc5b144f06939cf3a168f33143db0b7249dc8d3f1cdfc4cc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f94b0f59c6577491c9c0b6dc273f393461bde6e63ee27ede6053c768c5ad9c23",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2005-05-14T14:00:03Z",
    "title_canon_sha256": "ce7ef97d248dd2a2ff0c083cf910a68a2aee7ae3e07f9240f538d5b14a80ec36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505308",
    "kind": "arxiv",
    "version": 2
  }
}