Pith Number

pith:4ZQ2A55U

pith:2008:4ZQ2A55UUVHZNQSNZBBQYNMHVW

not attested not anchored not stored refs pending

Lyapunov spectrum for rational maps

Feliks Przytycki, Katrin Gelfert, Michal Rams

arxiv:0809.3363 v3 · 2008-09-19 · 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{4ZQ2A55UUVHZNQSNZBBQYNMHVW}

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	2026-05-18T04:39:39.458915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e661a077b4a54f96c24dc8430c3587ad834327053086d86803b1e090ee4c0bb3

Aliases

arxiv: 0809.3363 · arxiv_version: 0809.3363v3 · doi: 10.48550/arxiv.0809.3363 · pith_short_12: 4ZQ2A55UUVHZ · pith_short_16: 4ZQ2A55UUVHZNQSN · pith_short_8: 4ZQ2A55U

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/4ZQ2A55UUVHZNQSNZBBQYNMHVW \
  | 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: e661a077b4a54f96c24dc8430c3587ad834327053086d86803b1e090ee4c0bb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "225d1584a08e79aacec2518aef6ddbe1f2316e92bb029c437a7e7e71c196cec8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2008-09-19T12:37:43Z",
    "title_canon_sha256": "4c067c44ff53016b5bccbfaa1d177c8dcbec7cbe37ef29a0854bfc29f12db1fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.3363",
    "kind": "arxiv",
    "version": 3
  }
}