Pith Number

pith:TPTXBOAN

pith:2005:TPTXBOANIE5S22AD6QIHMC3UM7

not attested not anchored not stored refs pending

Taylor series expansions for the entropy rate of Hidden Markov Processes

Eytan Domany, Ido Kanter, Michael Aizenman, Or Zuk

arxiv:cs/0510005 v1 · 2005-10-03 · cs.IT · cond-mat.stat-mech · 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{TPTXBOANIE5S22AD6QIHMC3UM7}

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	2026-05-18T00:58:26.696643Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9be770b80d413b2d6803f410760b7467ec44d7df542d1af2bfcd284ee342e1af

Aliases

arxiv: cs/0510005 · arxiv_version: cs/0510005v1 · doi: 10.48550/arxiv.cs/0510005 · pith_short_12: TPTXBOANIE5S · pith_short_16: TPTXBOANIE5S22AD · pith_short_8: TPTXBOAN

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/TPTXBOANIE5S22AD6QIHMC3UM7 \
  | 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: 9be770b80d413b2d6803f410760b7467ec44d7df542d1af2bfcd284ee342e1af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e405f6359bd3bc6d662d75d2d30059f4a382938c822483cf887469ded957581",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.IT"
    ],
    "license": "",
    "primary_cat": "cs.IT",
    "submitted_at": "2005-10-03T09:56:37Z",
    "title_canon_sha256": "bab9330ebf44bdb25870c8ad999958cfebaf4f6777cf9bd0856d30fd998f3a96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cs/0510005",
    "kind": "arxiv",
    "version": 1
  }
}