Pith Number

pith:MJOIJLFU

pith:2010:MJOIJLFUCOYQKKFNCOBZCMSV3N

not attested not anchored not stored refs pending

Strong renewal theorems and Lyapunov spectra for $\alpha$-Farey and $\alpha$-L\"uroth systems

Bernd O. Stratmann, Marc Kesseb\"ohmer, Sara Munday

arxiv:1006.5693 v2 · 2010-06-29 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MJOIJLFUCOYQKKFNCOBZCMSV3N}

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	2026-05-18T00:33:33.149311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

625c84acb413b10528ad1383913255db6d6a4bb745b5995120b0f930b68772d6

Aliases

arxiv: 1006.5693 · arxiv_version: 1006.5693v2 · doi: 10.48550/arxiv.1006.5693 · pith_short_12: MJOIJLFUCOYQ · pith_short_16: MJOIJLFUCOYQKKFN · pith_short_8: MJOIJLFU

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/MJOIJLFUCOYQKKFNCOBZCMSV3N \
  | 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: 625c84acb413b10528ad1383913255db6d6a4bb745b5995120b0f930b68772d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8532019b838f53cdc374e47ad495597651d3d56c219b6ccbee79e731110186d3",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-06-29T17:59:51Z",
    "title_canon_sha256": "ed5a381a40d74ebf80a0009871c9f286acfce1ef8b5cfa12c9b3a4c1e16e1209"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.5693",
    "kind": "arxiv",
    "version": 2
  }
}