Pith Number

pith:ASK7CXBA

pith:2012:ASK7CXBA6RPYDY4Y4DSAD7A6TY

not attested not anchored not stored refs pending

Regularity and convergence rates for the Lyapunov exponents of linear co-cycles

W. Schlag

arxiv:1211.0648 v1 · 2012-11-03 · math.DS · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ASK7CXBA6RPYDY4Y4DSAD7A6TY}

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	2026-05-18T03:41:32.934635Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0495f15c20f45f81e398e0e401fc1e9e015c48c471afda38c36a73f761cb5c33

Aliases

arxiv: 1211.0648 · arxiv_version: 1211.0648v1 · doi: 10.48550/arxiv.1211.0648 · pith_short_12: ASK7CXBA6RPY · pith_short_16: ASK7CXBA6RPYDY4Y · pith_short_8: ASK7CXBA

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/ASK7CXBA6RPYDY4Y4DSAD7A6TY \
  | 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: 0495f15c20f45f81e398e0e401fc1e9e015c48c471afda38c36a73f761cb5c33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1834259932dd399b3e36aa83ec87f0b4d935a5def00ae57f43f44d1db8093832",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-11-03T23:03:25Z",
    "title_canon_sha256": "7714db87f46a387885a502d111f02eb69cac825d8eb335540133e4bf4bf18c98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0648",
    "kind": "arxiv",
    "version": 1
  }
}