Pith Number

pith:3ZTTM2QK

pith:2013:3ZTTM2QKJZQZUKLTR4MXKUHNFE

not attested not anchored not stored refs pending

Continuity of the Lyapunov exponents for quasiperiodic cocycles

Pedro Duarte, Silvius Klein

arxiv:1305.7504 v2 · 2013-05-31 · 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{3ZTTM2QKJZQZUKLTR4MXKUHNFE}

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	2026-05-18T02:41:10.311505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de67366a0a4e619a29738f197550ed292372442c79def5bfb8bbc51a47843439

Aliases

arxiv: 1305.7504 · arxiv_version: 1305.7504v2 · doi: 10.48550/arxiv.1305.7504 · pith_short_12: 3ZTTM2QKJZQZ · pith_short_16: 3ZTTM2QKJZQZUKLT · pith_short_8: 3ZTTM2QK

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/3ZTTM2QKJZQZUKLTR4MXKUHNFE \
  | 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: de67366a0a4e619a29738f197550ed292372442c79def5bfb8bbc51a47843439

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8dbd58570493215e83cafc2f76da307ba94a69e2ec984fb58ef63122941e811f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-05-31T18:54:37Z",
    "title_canon_sha256": "454e0802bfb5cebc28afd269ee4ea972f7aec5d2d0963e9a90d129fe45e1cba9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.7504",
    "kind": "arxiv",
    "version": 2
  }
}