Pith Number

pith:5RADZSFI

pith:2012:5RADZSFIBFZVMZXRQFPP264WLZ

not attested not anchored not stored refs pending

A coding-free simplicity criterion for the Lyapunov exponents of Teichmueller curves

Alex Eskin, Carlos Matheus

arxiv:1210.2157 v3 · 2012-10-08 · 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{5RADZSFIBFZVMZXRQFPP264WLZ}

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	2026-05-18T01:12:59.864176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec403cc8a809735666f1815efd7b965e41a53e3273963c122c972c2f7ce24b9f

Aliases

arxiv: 1210.2157 · arxiv_version: 1210.2157v3 · doi: 10.48550/arxiv.1210.2157 · pith_short_12: 5RADZSFIBFZV · pith_short_16: 5RADZSFIBFZVMZXR · pith_short_8: 5RADZSFI

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/5RADZSFIBFZVMZXRQFPP264WLZ \
  | 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: ec403cc8a809735666f1815efd7b965e41a53e3273963c122c972c2f7ce24b9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac97746dc8bfeca6affff6dfa3f4a0b8a9e72481f5882149b5b54a74033d8cfa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-08T06:55:48Z",
    "title_canon_sha256": "759259d27943a255c6330961fbd972c1fdc928ee2b75b5720213c8cce30382a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2157",
    "kind": "arxiv",
    "version": 3
  }
}