Pith Number

pith:YBFVBLTX

pith:2011:YBFVBLTXFT273RLZT6JTXPB2HK

not attested not anchored not stored refs pending

A Class of Markov Chains with no Spectral Gap

Nicholas Michalowski, Yevgeniy Kovchegov

arxiv:1109.6050 v2 · 2011-09-27 · math.CA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YBFVBLTXFT273RLZT6JTXPB2HK}

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	2026-05-18T04:02:25.100647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c04b50ae772cf5fdc5799f933bbc3a3a90c38137f198b0d5e1fbd307d9462602

Aliases

arxiv: 1109.6050 · arxiv_version: 1109.6050v2 · doi: 10.48550/arxiv.1109.6050 · pith_short_12: YBFVBLTXFT27 · pith_short_16: YBFVBLTXFT273RLZ · pith_short_8: YBFVBLTX

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/YBFVBLTXFT273RLZT6JTXPB2HK \
  | 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: c04b50ae772cf5fdc5799f933bbc3a3a90c38137f198b0d5e1fbd307d9462602

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0adb4ec20f8d19ab01912c74b60a2b13bff93717b70647cd72f4a2be231b7622",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-09-27T21:59:21Z",
    "title_canon_sha256": "702641027a819c2744682997f261f14c801c38c879e2b41b6e4228d8a94ce322"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6050",
    "kind": "arxiv",
    "version": 2
  }
}