Pith Number

pith:GEJ5J6JK

pith:2016:GEJ5J6JKBHVJSVZZZ7ZXOO2RGW

not attested not anchored not stored refs pending

Amenability, definable groups, and automorphism groups

Anand Pillay, Krzysztof Krupinski

arxiv:1612.07560 v2 · 2016-12-22 · math.LO · math.DS · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GEJ5J6JKBHVJSVZZZ7ZXOO2RGW}

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	2026-05-17T23:56:39.123580Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3113d4f92a09ea995739cff3773b51358bc67006e7ceb3ad82ac0d9de2919846

Aliases

arxiv: 1612.07560 · arxiv_version: 1612.07560v2 · doi: 10.48550/arxiv.1612.07560 · pith_short_12: GEJ5J6JKBHVJ · pith_short_16: GEJ5J6JKBHVJSVZZ · pith_short_8: GEJ5J6JK

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/GEJ5J6JKBHVJSVZZZ7ZXOO2RGW \
  | 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: 3113d4f92a09ea995739cff3773b51358bc67006e7ceb3ad82ac0d9de2919846

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ab378621fc2dac1bef68e3d63e0fac0796a4ac08fc560f2f5f4615ee5f31c1f",
    "cross_cats_sorted": [
      "math.DS",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2016-12-22T12:03:48Z",
    "title_canon_sha256": "8056e25f9200a62f53f4b272d2e0044d14bce1c2b4e23503b6e6cbe25ef11172"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07560",
    "kind": "arxiv",
    "version": 2
  }
}