Pith Number

pith:AFYQS3EC

pith:2012:AFYQS3EC6D6VMSVIOQDOKJMFPL

not attested not anchored not stored refs pending

Analyticity of Entropy Rate of Continuous-State Hidden Markov Chains

Brian Marcus, Guangyue Han

arxiv:1208.3261 v1 · 2012-08-16 · 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{AFYQS3EC6D6VMSVIOQDOKJMFPL}

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	2026-05-18T03:48:36.384090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0171096c82f0fd564aa87406e525857ae2f06a3c51bc27eb516bef452023ed91

Aliases

arxiv: 1208.3261 · arxiv_version: 1208.3261v1 · doi: 10.48550/arxiv.1208.3261 · pith_short_12: AFYQS3EC6D6V · pith_short_16: AFYQS3EC6D6VMSVI · pith_short_8: AFYQS3EC

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/AFYQS3EC6D6VMSVIOQDOKJMFPL \
  | 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: 0171096c82f0fd564aa87406e525857ae2f06a3c51bc27eb516bef452023ed91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b48f2a5b7fb9269ddc43c7eea6ed5fb989edb10ad025a4bedd645aa019969b6",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-08-16T01:45:22Z",
    "title_canon_sha256": "916ead3fb302503515425ccbaa20215c8703df7a4ec95fcbb1f7b80c9beec8bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3261",
    "kind": "arxiv",
    "version": 1
  }
}