Pith Number

pith:SWMJL7JG

pith:2013:SWMJL7JGVDPUMGXW2M4XCTHYES

not attested not anchored not stored refs pending

Quantitative approximations of the Lyapunov exponent of a rational function over valued fields

Y\^usuke Okuyama

arxiv:1309.2479 v3 · 2013-09-10 · math.DS · math.CV · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SWMJL7JGVDPUMGXW2M4XCTHYES}

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	2026-05-18T00:44:29.527677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

959895fd26a8df461af6d339714cf8248f1fdad2e3f389498855b47bde75dccd

Aliases

arxiv: 1309.2479 · arxiv_version: 1309.2479v3 · doi: 10.48550/arxiv.1309.2479 · pith_short_12: SWMJL7JGVDPU · pith_short_16: SWMJL7JGVDPUMGXW · pith_short_8: SWMJL7JG

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/SWMJL7JGVDPUMGXW2M4XCTHYES \
  | 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: 959895fd26a8df461af6d339714cf8248f1fdad2e3f389498855b47bde75dccd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08331827466dea26b7faf4a19a06ca2944014c09289dbc0447d23fa0a4fa2b78",
    "cross_cats_sorted": [
      "math.CV",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-09-10T12:27:51Z",
    "title_canon_sha256": "19a33f70700d315ba21132195013b22185afc19177ad36097a36168e494cc669"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.2479",
    "kind": "arxiv",
    "version": 3
  }
}