Pith Number

pith:WJ3LJMQC

pith:2010:WJ3LJMQCYHMQNUG3U3NHUSUALJ

not attested not anchored not stored refs pending

Local entropy theory for a countable discrete amenable group action

Guohua Zhang, Wen Huang, Xiangdong Ye

arxiv:1005.1335 v2 · 2010-05-08 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WJ3LJMQCYHMQNUG3U3NHUSUALJ}

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	2026-05-18T04:18:53.322097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b276b4b202c1d906d0dba6da7a4a805a4a20c0fdd321c99f1ebbc0843bea750e

Aliases

arxiv: 1005.1335 · arxiv_version: 1005.1335v2 · doi: 10.48550/arxiv.1005.1335 · pith_short_12: WJ3LJMQCYHMQ · pith_short_16: WJ3LJMQCYHMQNUG3 · pith_short_8: WJ3LJMQC

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/WJ3LJMQCYHMQNUG3U3NHUSUALJ \
  | 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: b276b4b202c1d906d0dba6da7a4a805a4a20c0fdd321c99f1ebbc0843bea750e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08022b84565e1708e89c1fdd9451fbaef6046059f1174595666e3c91ea74e7f0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-05-08T12:30:06Z",
    "title_canon_sha256": "fb933d2bb042d2b7e28ee0d9c5cb9d96b7ede929ff6f8f5f15db5a65da8b78db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.1335",
    "kind": "arxiv",
    "version": 2
  }
}