Pith Number

pith:IRBWJUEI

pith:2012:IRBWJUEI5O66BNZC5ORD7E4VDI

not attested not anchored not stored refs pending

Furstenberg entropy realizations for virtually free groups and lamplighter groups

Omer Tamuz, Yair Hartman

arxiv:1210.5897 v2 · 2012-10-22 · math.DS · 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{IRBWJUEI5O66BNZC5ORD7E4VDI}

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	2026-05-18T01:36:39.175391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

444364d088ebbde0b722eba23f93951a1241b4cbd4744fed3ba492678f485175

Aliases

arxiv: 1210.5897 · arxiv_version: 1210.5897v2 · doi: 10.48550/arxiv.1210.5897 · pith_short_12: IRBWJUEI5O66 · pith_short_16: IRBWJUEI5O66BNZC · pith_short_8: IRBWJUEI

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/IRBWJUEI5O66BNZC5ORD7E4VDI \
  | 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: 444364d088ebbde0b722eba23f93951a1241b4cbd4744fed3ba492678f485175

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79421cbbe72422b48ee33e779cfe3648ce8f882e34984be68c66a1a00c0817f2",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-22T13:36:03Z",
    "title_canon_sha256": "8f31108582fe88c491ac552e1c72e217b679c47e5f6691c0ab83bba8bb8b367a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5897",
    "kind": "arxiv",
    "version": 2
  }
}