Pith Number

pith:5TZAVJLU

pith:2018:5TZAVJLUYNJG3OROGTKILMC453

not attested not anchored not stored refs pending

Entropy, Lyapunov exponents, and rigidity of group actions

Aaron W. Brown, Bruno Santiago, Davi Obata, Dominique Malicet, Mario Rold\'an, Michele Triestino, S\'ebastien Alvarez

arxiv:1809.09192 v4 · 2018-09-24 · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5TZAVJLUYNJG3OROGTKILMC453}

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	2026-05-17T23:43:43.026275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ecf20aa574c3526dba2e34d485b05ceecec8cf7ca81a6e607345ad94fd20dcb4

Aliases

arxiv: 1809.09192 · arxiv_version: 1809.09192v4 · doi: 10.48550/arxiv.1809.09192 · pith_short_12: 5TZAVJLUYNJG · pith_short_16: 5TZAVJLUYNJG3ORO · pith_short_8: 5TZAVJLU

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/5TZAVJLUYNJG3OROGTKILMC453 \
  | 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: ecf20aa574c3526dba2e34d485b05ceecec8cf7ca81a6e607345ad94fd20dcb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59c0c6e235a265d6d4e167e97d7d6a659e975cc430c89219e4dc6ea7c078603d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-09-24T19:55:25Z",
    "title_canon_sha256": "579f82f19136b9ef39a471a6f7ba4eefe0d13f485667790550ba17d3706c6f88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.09192",
    "kind": "arxiv",
    "version": 4
  }
}