Pith Number

pith:4VTEYEYO

pith:2013:4VTEYEYOCTYKTK6US6WJFPDTNX

not attested not anchored not stored refs pending

Semisimplicity of the Lyapunov spectrum for irreducible cocycles

Alex Eskin, Carlos Matheus

arxiv:1309.0160 v4 · 2013-08-31 · 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{4VTEYEYOCTYKTK6US6WJFPDTNX}

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	2026-05-17T23:56:48.963010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5664c130e14f0a9abd497ac92bc736dd54f4440ce220f7e423794cff6199a3c

Aliases

arxiv: 1309.0160 · arxiv_version: 1309.0160v4 · doi: 10.48550/arxiv.1309.0160 · pith_short_12: 4VTEYEYOCTYK · pith_short_16: 4VTEYEYOCTYKTK6U · pith_short_8: 4VTEYEYO

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/4VTEYEYOCTYKTK6US6WJFPDTNX \
  | 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: e5664c130e14f0a9abd497ac92bc736dd54f4440ce220f7e423794cff6199a3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f955642238c0888c697df5915ae3fd67d65faea4d473b12a2bfb7bd4cec5890",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-08-31T21:30:45Z",
    "title_canon_sha256": "338ecf0d88ac6bb928b48aba53354370afbb879d6b6850445699f20a5bd823cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0160",
    "kind": "arxiv",
    "version": 4
  }
}