Pith Number

pith:A22TMM4J

pith:2011:A22TMM4J5VUTOLH7QVC5HNCI7R

not attested not anchored not stored refs pending

Low and Upper Bound of Approximate Sequence for the Entropy Rate of Binary Hidden Markov Processes

Jun Li, Mi Zhou, Shuangping Chen

arxiv:1112.6231 v1 · 2011-12-29 · 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{A22TMM4J5VUTOLH7QVC5HNCI7R}

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	2026-05-18T04:05:36.453724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06b5363389ed69372cff8545d3b448fc57bdc252542fc07ef9e9b7e1198169e0

Aliases

arxiv: 1112.6231 · arxiv_version: 1112.6231v1 · doi: 10.48550/arxiv.1112.6231 · pith_short_12: A22TMM4J5VUT · pith_short_16: A22TMM4J5VUTOLH7 · pith_short_8: A22TMM4J

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/A22TMM4J5VUTOLH7QVC5HNCI7R \
  | 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: 06b5363389ed69372cff8545d3b448fc57bdc252542fc07ef9e9b7e1198169e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c24e88e87a1076203e521a4fce9afc3562b9500ef2ab56398d3530b84c44eb09",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2011-12-29T05:36:48Z",
    "title_canon_sha256": "d47d79e05a524ed80233efe0f12a6bd71a462d3c9ef67c66269eace24421e0b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6231",
    "kind": "arxiv",
    "version": 1
  }
}