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Pith Number

pith:F3LJDD7X

pith:2013:F3LJDD7X6NQHGJKUTJZQZ5GJRV
not attested not anchored not stored refs pending

Uniform Positivity and Continuity of Lyapunov Exponents for a Class of $C^2$ Quasiperiodic Schr\"odinger Cocycles 

Yiqian Wang, Zhenghe Zhang

arxiv:1311.4282 v3 · 2013-11-18 · 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{F3LJDD7X6NQHGJKUTJZQZ5GJRV}

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 2026-05-18T03:03:46.770997Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

2ed6918ff7f3607325549a730cf4c98d59620356c0fcbf89067ebe21041a1483

Aliases

arxiv: 1311.4282 · arxiv_version: 1311.4282v3 · doi: 10.48550/arxiv.1311.4282 · pith_short_12: F3LJDD7X6NQH · pith_short_16: F3LJDD7X6NQHGJKU · pith_short_8: F3LJDD7X
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/F3LJDD7X6NQHGJKUTJZQZ5GJRV \
  | 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: 2ed6918ff7f3607325549a730cf4c98d59620356c0fcbf89067ebe21041a1483
Canonical record JSON 
{
  "metadata": {
    "abstract_canon_sha256": "1d711419c0de060be8d40313f933db1f3660d56adbd8a2f8665c490228132545",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-11-18T07:13:52Z",
    "title_canon_sha256": "d6e32f23ad60294a821beab966d9b317663d7d6ccb2e960b0ad3315df84f5eb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.4282",
    "kind": "arxiv",
    "version": 3
  }
}