Pith Number

pith:TMVOGJF6

pith:2016:TMVOGJF6TNZVUHFZJOIZ4Y2KHF

not attested not anchored not stored refs pending

Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases

Carlos Matheus, Disheng Xu, Jairo Bochi, Mario Bessa, Michel Cambrainha, Paulo Varandas

arxiv:1611.10158 v1 · 2016-11-30 · 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{TMVOGJF6TNZVUHFZJOIZ4Y2KHF}

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	2026-05-18T00:56:11.068598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b2ae324be9b735a1cb94b919e634a395c3dc127578d9a78817a9a5c58347e43

Aliases

arxiv: 1611.10158 · arxiv_version: 1611.10158v1 · doi: 10.48550/arxiv.1611.10158 · pith_short_12: TMVOGJF6TNZV · pith_short_16: TMVOGJF6TNZVUHFZ · pith_short_8: TMVOGJF6

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/TMVOGJF6TNZVUHFZJOIZ4Y2KHF \
  | 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: 9b2ae324be9b735a1cb94b919e634a395c3dc127578d9a78817a9a5c58347e43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ace862822a3f8bf4fe1ce437d0ae167cf04864ff8ac8c07856a29198b33f1e7c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-11-30T14:13:35Z",
    "title_canon_sha256": "cb32c490fc605b857fef098475784d6e1b35db89f58c212b14ec885b45576151"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.10158",
    "kind": "arxiv",
    "version": 1
  }
}