Pith Number

pith:4HBOK2M4

pith:2012:4HBOK2M4DIBPVC2BZL7XWFCIRD

not attested not anchored not stored refs pending

A Banach space-valued ergodic theorem for amenable groups and applications

Fabian Schwarzenberger, Felix Pogorzelski

arxiv:1205.3649 v2 · 2012-05-16 · math.SP · math-ph · math.DS · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4HBOK2M4DIBPVC2BZL7XWFCIRD}

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	2026-05-18T03:17:14.828123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1c2e5699c1a02fa8b41caff7b144888d2ae5906b20265b55c1dc902ecead2cc

Aliases

arxiv: 1205.3649 · arxiv_version: 1205.3649v2 · doi: 10.48550/arxiv.1205.3649 · pith_short_12: 4HBOK2M4DIBP · pith_short_16: 4HBOK2M4DIBPVC2B · pith_short_8: 4HBOK2M4

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/4HBOK2M4DIBPVC2BZL7XWFCIRD \
  | 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: e1c2e5699c1a02fa8b41caff7b144888d2ae5906b20265b55c1dc902ecead2cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5f0c79abf1b577fab5ca1ca6448e7782d41497446de0e935a271c5c789a30f2",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-05-16T12:08:20Z",
    "title_canon_sha256": "fdcf7f54c09857700fc0cbcbeb91c5c1a89798a3956be8bd25e7dfbcd2fc9d53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3649",
    "kind": "arxiv",
    "version": 2
  }
}