Pith Number

pith:ULEXO7Z2

pith:2012:ULEXO7Z2C3AFQFEFGBBF6SSJUH

not attested not anchored not stored refs pending

Induced quasi-cocycles on groups with hyperbolically embedded subgroups

D. Osin, M. Hull

arxiv:1203.5436 v4 · 2012-03-24 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ULEXO7Z2C3AFQFEFGBBF6SSJUH}

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	2026-05-18T02:41:43.298502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2c9777f3a16c058148530425f4a49a1d7c980b2b0450c94eb6eb1ee75f9bc73

Aliases

arxiv: 1203.5436 · arxiv_version: 1203.5436v4 · doi: 10.48550/arxiv.1203.5436 · pith_short_12: ULEXO7Z2C3AF · pith_short_16: ULEXO7Z2C3AFQFEF · pith_short_8: ULEXO7Z2

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/ULEXO7Z2C3AFQFEFGBBF6SSJUH \
  | 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: a2c9777f3a16c058148530425f4a49a1d7c980b2b0450c94eb6eb1ee75f9bc73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2cf0c818c6ef7f13ad740c43fd533ee79de278bac0a0d92b2e9b376652816947",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-03-24T18:27:33Z",
    "title_canon_sha256": "b8aae12b43760947cf3707768c35176514fc1e129a988f06c4ee1813efc539a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5436",
    "kind": "arxiv",
    "version": 4
  }
}