Pith Number

pith:ZIMBT3GJ

pith:2016:ZIMBT3GJTG4PMFYYWATYRHRJC6

not attested not anchored not stored refs pending

Metastable distributions of Markov chains with rare transitions

Leonid Koralov, Mark Freidlin

arxiv:1607.07866 v1 · 2016-07-26 · 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{ZIMBT3GJTG4PMFYYWATYRHRJC6}

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	2026-05-18T00:45:48.861301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca1819ecc999b8f61718b027889e2917bc21909385f2b0a6e763394782a9473d

Aliases

arxiv: 1607.07866 · arxiv_version: 1607.07866v1 · doi: 10.48550/arxiv.1607.07866 · pith_short_12: ZIMBT3GJTG4P · pith_short_16: ZIMBT3GJTG4PMFYY · pith_short_8: ZIMBT3GJ

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/ZIMBT3GJTG4PMFYYWATYRHRJC6 \
  | 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: ca1819ecc999b8f61718b027889e2917bc21909385f2b0a6e763394782a9473d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2eb1497f2a0cc10ade864562c50ba7400abd1b34044ede0445c13be33af13f9d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-07-26T19:59:16Z",
    "title_canon_sha256": "14edb7ab01240ab0f4306b913e67f546da11320ed0f90e10b5c603986bb717fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.07866",
    "kind": "arxiv",
    "version": 1
  }
}