Pith Number

pith:MZGW7C6O

pith:2016:MZGW7C6OUVQHZRG3OG3SV7W3YE

not attested not anchored not stored refs pending

Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocycles

Pedro Duarte, Silvius Klein

arxiv:1603.06851 v3 · 2016-03-22 · math.DS · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MZGW7C6OUVQHZRG3OG3SV7W3YE}

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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.

Cited by

1 paper in Pith

Random product of quasi-periodic cocycles

Receipt and verification

First computed	2026-05-18T00:48:37.399449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

664d6f8bcea5607cc4db71b72afedbc138d6a0dd84e32dc3a3235ade0ba009ca

Aliases

arxiv: 1603.06851 · arxiv_version: 1603.06851v3 · doi: 10.48550/arxiv.1603.06851 · pith_short_12: MZGW7C6OUVQH · pith_short_16: MZGW7C6OUVQHZRG3 · pith_short_8: MZGW7C6O

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/MZGW7C6OUVQHZRG3OG3SV7W3YE \
  | 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: 664d6f8bcea5607cc4db71b72afedbc138d6a0dd84e32dc3a3235ade0ba009ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89618df11c34a869acbb1202afb804cd2eef39b5d8470ef0d76767c4ef6fd181",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-03-22T16:10:58Z",
    "title_canon_sha256": "ce47c497bf61f987cc7d919f6da2d6662415991c244fc9422d3a82d887bbdd07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.06851",
    "kind": "arxiv",
    "version": 3
  }
}