Pith Number

pith:3YJZPVZO

pith:2015:3YJZPVZO4QXXRATQSTHKU2FMA5

not attested not anchored not stored refs pending

Ergodic Properties of the Random Walk Adic Transformation over the Beta Transformation

Michael Bromberg

arxiv:1511.02482 v2 · 2015-11-08 · 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{3YJZPVZO4QXXRATQSTHKU2FMA5}

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	2026-05-18T01:26:17.591089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de1397d72ee42f78827094ceaa68ac077cea4d0b6f28ef051ab5bf5eba5852cb

Aliases

arxiv: 1511.02482 · arxiv_version: 1511.02482v2 · doi: 10.48550/arxiv.1511.02482 · pith_short_12: 3YJZPVZO4QXX · pith_short_16: 3YJZPVZO4QXXRATQ · pith_short_8: 3YJZPVZO

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/3YJZPVZO4QXXRATQSTHKU2FMA5 \
  | 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: de1397d72ee42f78827094ceaa68ac077cea4d0b6f28ef051ab5bf5eba5852cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c398f20551f5685cde2f184cffcc83e5ee2b6d99263b39e1e0740d3240fa1fe8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-11-08T13:19:25Z",
    "title_canon_sha256": "bc6d45585a9e453a9e46245b10884760a9071a4fd71cb8c30af4e89dfab5b032"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02482",
    "kind": "arxiv",
    "version": 2
  }
}