Pith Number

pith:G2FMBYEQ

pith:2016:G2FMBYEQYA57J4H5QTHJPQV4QF

not attested not anchored not stored refs pending

Entropy spectrum of Lyapunov exponents for nonhyperbolic step skew-products and elliptic cocycles

Katrin Gelfert, Lorenzo J. D\'iaz, Micha{\l} Rams

arxiv:1610.07167 v2 · 2016-10-23 · 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{G2FMBYEQYA57J4H5QTHJPQV4QF}

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	2026-05-18T00:32:31.254934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

368ac0e090c03bf4f0fd84ce97c2bc81685e69fca1ed90c285377472546bf8b3

Aliases

arxiv: 1610.07167 · arxiv_version: 1610.07167v2 · doi: 10.48550/arxiv.1610.07167 · pith_short_12: G2FMBYEQYA57 · pith_short_16: G2FMBYEQYA57J4H5 · pith_short_8: G2FMBYEQ

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/G2FMBYEQYA57J4H5QTHJPQV4QF \
  | 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: 368ac0e090c03bf4f0fd84ce97c2bc81685e69fca1ed90c285377472546bf8b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92d4b4889ab12b303138d0d29eeada7b47f1a481caad7195e33068ef07cea5d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-10-23T13:34:08Z",
    "title_canon_sha256": "ec5b16168e7a991ea2978ce07cb6f5d3f2ebc1c6bb2d1ce38dd60ae7b714f483"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.07167",
    "kind": "arxiv",
    "version": 2
  }
}