Pith Number

pith:77UWYHPC

pith:2015:77UWYHPCOV6R7FKUKYQT2Z7NQI

not attested not anchored not stored refs pending

Nonexistence of Lyapunov Exponents for Matrix Cocycles

Xueting Tian

arxiv:1505.04477 v1 · 2015-05-18 · 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{77UWYHPCOV6R7FKUKYQT2Z7NQI}

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	2026-05-18T00:50:52.523021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffe96c1de2757d1f955456213d67ed8221ddd4e4dcefe62d320ba5c580bea5fa

Aliases

arxiv: 1505.04477 · arxiv_version: 1505.04477v1 · doi: 10.48550/arxiv.1505.04477 · pith_short_12: 77UWYHPCOV6R · pith_short_16: 77UWYHPCOV6R7FKU · pith_short_8: 77UWYHPC

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/77UWYHPCOV6R7FKUKYQT2Z7NQI \
  | 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: ffe96c1de2757d1f955456213d67ed8221ddd4e4dcefe62d320ba5c580bea5fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "306d9e7173d4d0af718ad2c39ba61a9da69460d7ac42c9cc9309fd0c458c642a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-05-18T00:02:09Z",
    "title_canon_sha256": "6ef338c8bc5dbd402e8c862095f291761b083397aa7752833677af8c22ad1af0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04477",
    "kind": "arxiv",
    "version": 1
  }
}