Pith Number

pith:DUPALEVE

pith:2004:DUPALEVEPFG4J74SLS226UGZL6

not attested not anchored not stored refs pending

Topological invariance of the sign of the Lyapunov exponents in one-dimensional maps

Henk Bruin, Stefano Luzzatto

arxiv:math/0409084 v3 · 2004-09-06 · math.DS · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DUPALEVEPFG4J74SLS226UGZL6}

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	2026-07-04T14:39:02.566980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d1e0592a4794dc4ff925cb5af50d95f86bea5fc481d806b31dbf0d5560a3e79

Aliases

arxiv: math/0409084 · arxiv_version: math/0409084v3 · doi: 10.48550/arxiv.math/0409084 · pith_short_12: DUPALEVEPFG4 · pith_short_16: DUPALEVEPFG4J74S · pith_short_8: DUPALEVE

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/DUPALEVEPFG4J74SLS226UGZL6 \
  | 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: 1d1e0592a4794dc4ff925cb5af50d95f86bea5fc481d806b31dbf0d5560a3e79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92846dc1b886922853e7c7147870cdc388e786b26937ab877a76888fd247d1bc",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2004-09-06T14:38:19Z",
    "title_canon_sha256": "c03b4987e3f50b0f00fd4820884a71a1735eb832911e7ccc6d5fafbfe468cc33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0409084",
    "kind": "arxiv",
    "version": 3
  }
}