Pith Number

pith:ZVOHZAWW

pith:2005:ZVOHZAWWMY5FCFK3IG72KWYML5

not attested not anchored not stored refs pending

Finitely presentable, non-Hopfian groups with Kazhdan's Property (T) and infinite outer automorphism group

Yves de Cornulier

arxiv:math/0502140 v4 · 2005-02-07 · 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{ZVOHZAWWMY5FCFK3IG72KWYML5}

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	2026-05-18T03:37:29.326949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd5c7c82d6663a51155b41bfa55b0c5f4eae7a6d3bb80b49eb152d72a9e0633a

Aliases

arxiv: math/0502140 · arxiv_version: math/0502140v4 · doi: 10.48550/arxiv.math/0502140 · pith_short_12: ZVOHZAWWMY5F · pith_short_16: ZVOHZAWWMY5FCFK3 · pith_short_8: ZVOHZAWW

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/ZVOHZAWWMY5FCFK3IG72KWYML5 \
  | 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: cd5c7c82d6663a51155b41bfa55b0c5f4eae7a6d3bb80b49eb152d72a9e0633a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "989e0d2f6aeca4a1da0fe5df734978ac38782f69fcd4d2681928afdb5cfeb191",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2005-02-07T18:46:03Z",
    "title_canon_sha256": "0e8d3d1e39ba1a128c766bcc5975e0a6f12aabfae68b51ec965dccdbf0f60c25"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0502140",
    "kind": "arxiv",
    "version": 4
  }
}