Pith Number

pith:5BQZVKNE

pith:2009:5BQZVKNEOKRRQVERO27RIUYANB

not attested not anchored not stored refs pending

Lyapunov spectrum of asymptotically sub-additive potentials

De-Jun Feng, Wen Hunag

arxiv:0905.2680 v2 · 2009-05-16 · 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{5BQZVKNEOKRRQVERO27RIUYANB}

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	2026-05-18T02:13:39.113158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8619aa9a472a318549176bf14530068429c0b7e22727ae21b818238a883938c

Aliases

arxiv: 0905.2680 · arxiv_version: 0905.2680v2 · doi: 10.48550/arxiv.0905.2680 · pith_short_12: 5BQZVKNEOKRR · pith_short_16: 5BQZVKNEOKRRQVER · pith_short_8: 5BQZVKNE

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/5BQZVKNEOKRRQVERO27RIUYANB \
  | 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: e8619aa9a472a318549176bf14530068429c0b7e22727ae21b818238a883938c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f25fed8a0975fdba4252b15177adab3bcc24ec7df607da88de880e6b407ab406",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-05-16T12:32:05Z",
    "title_canon_sha256": "48dd6b4bdb04c45a7c0d72353f41e9793268cfe2835937d60fb579d261ec4045"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.2680",
    "kind": "arxiv",
    "version": 2
  }
}