Pith Number

pith:5IWWT5HM

pith:2011:5IWWT5HMC343LEDYSROYDZKWFD

not attested not anchored not stored refs pending

H\"older continuity of Lyapunov exponent for quasi-periodic Jacobi operators

Kai Tao

arxiv:1108.3747 v1 · 2011-08-18 · 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{5IWWT5HMC343LEDYSROYDZKWFD}

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	2026-05-18T04:15:07.536538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea2d69f4ec16f9b59078945d81e55628f453ce524b771d11082c9c2f85a6a5d8

Aliases

arxiv: 1108.3747 · arxiv_version: 1108.3747v1 · doi: 10.48550/arxiv.1108.3747 · pith_short_12: 5IWWT5HMC343 · pith_short_16: 5IWWT5HMC343LEDY · pith_short_8: 5IWWT5HM

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/5IWWT5HMC343LEDYSROYDZKWFD \
  | 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: ea2d69f4ec16f9b59078945d81e55628f453ce524b771d11082c9c2f85a6a5d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41b1a0d4c14e701bf5c89a46b43cdd349bec59a6b379f2298fe32bca9be00041",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-08-18T13:06:16Z",
    "title_canon_sha256": "a1c3ab628038d002bf24944d88fe2ccbdd8a93db55605fd1b70dd209457d9111"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3747",
    "kind": "arxiv",
    "version": 1
  }
}