Pith Number

pith:RKQB5D5S

pith:2010:RKQB5D5S4LT4ZLB45UZUCE7ARP

not attested not anchored not stored refs pending

A new proof of the Herman-Avila-Bochi formula for Lyapunov exponents of SL(2,R)-cocycles

Alexandre T. Baraviera, Joao Lopes Dias, Pedro Duarte

arxiv:1004.4800 v1 · 2010-04-27 · 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{RKQB5D5S4LT4ZLB45UZUCE7ARP}

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	2026-05-18T02:07:53.248911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8aa01e8fb2e2e7ccac3ced334113e08bf8b8a6fd8ce450035d165f350093bafb

Aliases

arxiv: 1004.4800 · arxiv_version: 1004.4800v1 · doi: 10.48550/arxiv.1004.4800 · pith_short_12: RKQB5D5S4LT4 · pith_short_16: RKQB5D5S4LT4ZLB4 · pith_short_8: RKQB5D5S

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/RKQB5D5S4LT4ZLB45UZUCE7ARP \
  | 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: 8aa01e8fb2e2e7ccac3ced334113e08bf8b8a6fd8ce450035d165f350093bafb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78d660e6579c67eae9799c491bafd05952ea4e386dc9871d8c281b8031c26812",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-04-27T13:36:11Z",
    "title_canon_sha256": "15358fcd19bc8bf29592bf5df4ec953591caee3237c39b209b16a806c301eba3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4800",
    "kind": "arxiv",
    "version": 1
  }
}