Pith Number

pith:5F4KHDNX

pith:2014:5F4KHDNXXQXKEFWAHWKR7BA4N3

not attested not anchored not stored refs pending

A study of imprecise Markov chains: joint lower expectations and point-wise ergodic theorems

Gert de Cooman, Jasper De Bock, Stavros Lopatatzidis

arxiv:1411.4173 v3 · 2014-11-15 · 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{5F4KHDNXXQXKEFWAHWKR7BA4N3}

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	2026-05-18T01:22:48.733164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e978a38db7bc2ea216c03d951f841c6edcc53cfebd4dd50c860090e58df6d911

Aliases

arxiv: 1411.4173 · arxiv_version: 1411.4173v3 · doi: 10.48550/arxiv.1411.4173 · pith_short_12: 5F4KHDNXXQXK · pith_short_16: 5F4KHDNXXQXKEFWA · pith_short_8: 5F4KHDNX

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/5F4KHDNXXQXKEFWAHWKR7BA4N3 \
  | 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: e978a38db7bc2ea216c03d951f841c6edcc53cfebd4dd50c860090e58df6d911

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "026c6141f1ce3dcb8d1c80c95a5b1aa74a59dbd91296f12a0b31716e0de15698",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-11-15T18:50:20Z",
    "title_canon_sha256": "1d947768f705c5a1534bc10838013cb27dc40c7dc811d18fc4419935e417d92b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.4173",
    "kind": "arxiv",
    "version": 3
  }
}