Pith Number

pith:O5RWL4XD

pith:2019:O5RWL4XD5HTS44LKN3L4QAXZZX

not attested not anchored not stored refs pending

Flexibility of Lyapunov exponents

Anatole Katok, Federico Rodriguez Hertz, Jairo Bochi

arxiv:1908.07891 v2 · 2019-08-21 · 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{O5RWL4XD5HTS44LKN3L4QAXZZX}

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	2026-07-05T02:30:10.751559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

776365f2e3e9e72e716a6ed7c802f9cdf8188c42146027e8748e0f0b2ec16b93

Aliases

arxiv: 1908.07891 · arxiv_version: 1908.07891v2 · doi: 10.48550/arxiv.1908.07891 · pith_short_12: O5RWL4XD5HTS · pith_short_16: O5RWL4XD5HTS44LK · pith_short_8: O5RWL4XD

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/O5RWL4XD5HTS44LKN3L4QAXZZX \
  | 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: 776365f2e3e9e72e716a6ed7c802f9cdf8188c42146027e8748e0f0b2ec16b93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "168be50902b2eda4e1cd3b65ca7e2edb91f932f560218e69456bcfe166879f75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-08-21T14:25:53Z",
    "title_canon_sha256": "b8df6d4969ff2fde3e763fab0fa25aaab00f10a097b4c18562e5e5e74389f985"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07891",
    "kind": "arxiv",
    "version": 2
  }
}