Pith Number

pith:WQ347YFC

pith:2013:WQ347YFCO2Y7PVORUUJWLIQFEK

not attested not anchored not stored refs pending

The Fried average entropy and slow entropy for actions of higher rank abelian groups

Anatole Katok, Federico Rodriguez Hertz, Svetlana Katok

arxiv:1311.0927 v4 · 2013-11-04 · math.DS · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WQ347YFCO2Y7PVORUUJWLIQFEK}

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	2026-05-18T02:47:31.445242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b437cfe0a276b1f7d5d1a51365a20522aecb58c6d51566d89cb66dc91522d5b2

Aliases

arxiv: 1311.0927 · arxiv_version: 1311.0927v4 · doi: 10.48550/arxiv.1311.0927 · pith_short_12: WQ347YFCO2Y7 · pith_short_16: WQ347YFCO2Y7PVOR · pith_short_8: WQ347YFC

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/WQ347YFCO2Y7PVORUUJWLIQFEK \
  | 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: b437cfe0a276b1f7d5d1a51365a20522aecb58c6d51566d89cb66dc91522d5b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "816d65b93b3bbbe423d146262cd003b96e0994fab07aae3bdab8bc2e22d7f7cc",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-11-04T23:40:28Z",
    "title_canon_sha256": "463880215ea790642370db86e13e31c1f665e8348f1bb8cb67ec52b5ca85a9cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0927",
    "kind": "arxiv",
    "version": 4
  }
}