Pith Number

pith:3PVIUYS2

pith:2010:3PVIUYS2M3QEHH2DVBQYJDSEV6

not attested not anchored not stored refs pending

Sofic entropy and amenable groups

Lewis Bowen

arxiv:1008.1354 v2 · 2010-08-07 · 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{3PVIUYS2M3QEHH2DVBQYJDSEV6}

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	2026-05-18T04:25:39.106399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbea8a625a66e0439f43a861848e44afb333c395f675ff0f1521d5ec0f16c108

Aliases

arxiv: 1008.1354 · arxiv_version: 1008.1354v2 · doi: 10.48550/arxiv.1008.1354 · pith_short_12: 3PVIUYS2M3QE · pith_short_16: 3PVIUYS2M3QEHH2D · pith_short_8: 3PVIUYS2

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/3PVIUYS2M3QEHH2DVBQYJDSEV6 \
  | 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: dbea8a625a66e0439f43a861848e44afb333c395f675ff0f1521d5ec0f16c108

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "292e9f7ef8ac7d6c7a77257ce2d936f18e36b8c90ef3f3a3e23992de69fac6f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-08-07T16:48:33Z",
    "title_canon_sha256": "0341949598e22932f2403b2277e5fa5085de9877b0fa558e2982b865adb10bd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1354",
    "kind": "arxiv",
    "version": 2
  }
}