Pith Number

pith:LWYU24VE

pith:2008:LWYU24VEMDMHSBD4OFM6BTY33J

not attested not anchored not stored refs pending

T-entropy and Variational Principle for the spectral radius of transfer and weighted shift operators

A. B. Antonevich, A. V. Lebedev, V. I. Bakhtin

arxiv:0809.3116 v2 · 2008-09-18 · math.DS · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LWYU24VEMDMHSBD4OFM6BTY33J}

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	2026-05-18T04:11:52.108132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5db14d72a460d879047c7159e0cf1bda628e333961a85753f88327e9602656cc

Aliases

arxiv: 0809.3116 · arxiv_version: 0809.3116v2 · doi: 10.48550/arxiv.0809.3116 · pith_short_12: LWYU24VEMDMH · pith_short_16: LWYU24VEMDMHSBD4 · pith_short_8: LWYU24VE

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/LWYU24VEMDMHSBD4OFM6BTY33J \
  | 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: 5db14d72a460d879047c7159e0cf1bda628e333961a85753f88327e9602656cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cbe6791bfec79409b7ac86cbf3a2fd6289b41e269c1ffd61547cf575e91d2a6",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2008-09-18T09:39:58Z",
    "title_canon_sha256": "b32f020869ad8142306f04e78a48f153dd1cc7136f9a36d0af37c1d5cf90146c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.3116",
    "kind": "arxiv",
    "version": 2
  }
}