Pith Number

pith:B425XZZ5

pith:2011:B425XZZ5HILMZN6NWGAKHRKF2U

not attested not anchored not stored refs pending

Finitely presented groups with infinitely many non-homeomorphic asymptotic cones

Abderezak Ould Houcine, Denis Osin

arxiv:1108.2100 v4 · 2011-08-10 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B425XZZ5HILMZN6NWGAKHRKF2U}

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	2026-05-18T04:14:45.807250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f35dbe73d3a16ccb7cdb180a3c545d537a828d3aa3d732d42f153ae1e15279a

Aliases

arxiv: 1108.2100 · arxiv_version: 1108.2100v4 · doi: 10.48550/arxiv.1108.2100 · pith_short_12: B425XZZ5HILM · pith_short_16: B425XZZ5HILMZN6N · pith_short_8: B425XZZ5

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/B425XZZ5HILMZN6NWGAKHRKF2U \
  | 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: 0f35dbe73d3a16ccb7cdb180a3c545d537a828d3aa3d732d42f153ae1e15279a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8c4cd05946c71e5e331d9a53f16cfa7365d2e7951eff5e17a2b74849846fda2",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-08-10T06:00:37Z",
    "title_canon_sha256": "bd01a0046b014f543bb73d5136d308dbbb3cbcc58c6f2f947458ea039862c311"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.2100",
    "kind": "arxiv",
    "version": 4
  }
}