Pith Number

pith:67SLUJRQ

pith:2010:67SLUJRQFEYZZPW6ZOZ4N5YB3L

not attested not anchored not stored refs pending

Groups definable in o-minimal structures: structure theorem, G^000, definable amenability and bounded orbits

Anand Pillay

arxiv:1012.4640 v2 · 2010-12-21 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{67SLUJRQFEYZZPW6ZOZ4N5YB3L}

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	2026-05-18T04:31:52.092497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7e4ba263029319cbedecbb3c6f701dae7d75e77f6a29436d35892dd58b6a999

Aliases

arxiv: 1012.4640 · arxiv_version: 1012.4640v2 · doi: 10.48550/arxiv.1012.4640 · pith_short_12: 67SLUJRQFEYZ · pith_short_16: 67SLUJRQFEYZZPW6 · pith_short_8: 67SLUJRQ

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/67SLUJRQFEYZZPW6ZOZ4N5YB3L \
  | 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: f7e4ba263029319cbedecbb3c6f701dae7d75e77f6a29436d35892dd58b6a999

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a4690531a3a1ea480ac8a794b86b38d1157f738d75fd36d1f743990ba110216",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2010-12-21T13:00:03Z",
    "title_canon_sha256": "457e602b569e9facef57dbf57c4a811a3aa75a00a704c1f339ac74092e19b3d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4640",
    "kind": "arxiv",
    "version": 2
  }
}