Pith Number

pith:GIGLTNVT

pith:2009:GIGLTNVTJPQPMY2MRPA2B4HM4T

not attested not anchored not stored refs pending

A complete solution to Blackwell's unique ergodicity problem for hidden Markov chains

Pavel Chigansky, Ramon van Handel

arxiv:0910.3603 v2 · 2009-10-19 · math.PR · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GIGLTNVTJPQPMY2MRPA2B4HM4T}

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	2026-05-18T04:35:57.204047Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

320cb9b6b34be0f6634c8bc1a0f0ece4eed892575eb8c2c049fd6d14c73fba10

Aliases

arxiv: 0910.3603 · arxiv_version: 0910.3603v2 · doi: 10.48550/arxiv.0910.3603 · pith_short_12: GIGLTNVTJPQP · pith_short_16: GIGLTNVTJPQPMY2M · pith_short_8: GIGLTNVT

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/GIGLTNVTJPQPMY2MRPA2B4HM4T \
  | 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: 320cb9b6b34be0f6634c8bc1a0f0ece4eed892575eb8c2c049fd6d14c73fba10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4081ec7e2ff0e3831eda08c962815131030879b138fe018ca9d6770bc9e9d61d",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-10-19T15:57:41Z",
    "title_canon_sha256": "c26821523f178f8b3e22ae7e51200ad972ce1cf26c34fd97ab9cf7be08c6ac3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.3603",
    "kind": "arxiv",
    "version": 2
  }
}