Pith Number

pith:LJX6C6PM

pith:2011:LJX6C6PMVH6EUG5UO5UDNQDGVC

not attested not anchored not stored refs pending

On $L_1$-Weak Ergodicity of nonhomogeneous discrete Markov processes and its applications

Farrukh Mukhamedov

arxiv:1105.0478 v3 · 2011-05-03 · math.PR · 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{LJX6C6PMVH6EUG5UO5UDNQDGVC}

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	2026-05-18T03:58:24.737275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a6fe179eca9fc4a1bb4776836c066a8a03ff36e0ec3da97e1c994e45e7504df

Aliases

arxiv: 1105.0478 · arxiv_version: 1105.0478v3 · doi: 10.48550/arxiv.1105.0478 · pith_short_12: LJX6C6PMVH6E · pith_short_16: LJX6C6PMVH6EUG5U · pith_short_8: LJX6C6PM

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/LJX6C6PMVH6EUG5UO5UDNQDGVC \
  | 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: 5a6fe179eca9fc4a1bb4776836c066a8a03ff36e0ec3da97e1c994e45e7504df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8977b7a3cfbc213fd0c37d0a602f003677838d3cce2c68153af520e098fb32a",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-05-03T05:37:56Z",
    "title_canon_sha256": "4c98ce004d766c205b2e85d45cea4fab71631e4342e38a7639798ff09b6f5e98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.0478",
    "kind": "arxiv",
    "version": 3
  }
}