Pith Number

pith:KKMLCAKD

pith:2012:KKMLCAKDKGNQLYFDVMSXLVX2TN

not attested not anchored not stored refs pending

Group Extended Markov Systems, Amenability, and the Perron-Frobenius Operator

Johannes Jaerisch

arxiv:1205.5126 v4 · 2012-05-23 · math.DS · math.FA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KKMLCAKDKGNQLYFDVMSXLVX2TN}

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	2026-05-18T01:27:16.178873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5298b10143519b05e0a3ab2575d6fa9b6b25d1248fd0bf4f165e6752f679ace3

Aliases

arxiv: 1205.5126 · arxiv_version: 1205.5126v4 · doi: 10.48550/arxiv.1205.5126 · pith_short_12: KKMLCAKDKGNQ · pith_short_16: KKMLCAKDKGNQLYFD · pith_short_8: KKMLCAKD

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/KKMLCAKDKGNQLYFDVMSXLVX2TN \
  | 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: 5298b10143519b05e0a3ab2575d6fa9b6b25d1248fd0bf4f165e6752f679ace3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0add4b23a1320bc76b7f366fb4e0e474198136d413dc9bb2327e9d9d5314cc7b",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-05-23T08:29:31Z",
    "title_canon_sha256": "0deef2f41cc53caada29fa629d041896311002c03d913d29e06b4701fc11b666"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5126",
    "kind": "arxiv",
    "version": 4
  }
}