Pith Number

pith:Q2C7TDO6

pith:2007:Q2C7TDO63XA65FKQGKCJZP34XA

not attested not anchored not stored refs pending

Positive Lyapunov exponents and localization bounds for strongly mixing potentials

Christian Sadel, Hermann Schulz-Baldes

arxiv:math-ph/0702052 v1 · 2007-02-15 · 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{Q2C7TDO63XA65FKQGKCJZP34XA}

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	2026-05-18T04:31:00.345463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8685f98ddeddc1ee955032849cbf7cb8099d0a6eab356364ab1e6699874cfa6c

Aliases

arxiv: math-ph/0702052 · arxiv_version: math-ph/0702052v1 · doi: 10.48550/arxiv.math-ph/0702052 · pith_short_12: Q2C7TDO63XA6 · pith_short_16: Q2C7TDO63XA65FKQ · pith_short_8: Q2C7TDO6

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/Q2C7TDO63XA65FKQGKCJZP34XA \
  | 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: 8685f98ddeddc1ee955032849cbf7cb8099d0a6eab356364ab1e6699874cfa6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adcfe29eb75098d09eac0cb318c58822e3ea1f1321ee0a4194510854bfae5720",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2007-02-15T14:07:55Z",
    "title_canon_sha256": "5c4aff37fe8556c7d1aa6d8134f72de397d86c6fe1889d4b46e1de72bcf42ccf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0702052",
    "kind": "arxiv",
    "version": 1
  }
}