Pith Number

pith:XUL5GNW4

pith:2011:XUL5GNW4ORVJTRL4NNWLMXTEHR

not attested not anchored not stored refs pending

Divergence, thick groups, and short conjugators

Cornelia Drutu, Jason Behrstock

arxiv:1110.5005 v1 · 2011-10-22 · math.GT · 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{XUL5GNW4ORVJTRL4NNWLMXTEHR}

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	2026-05-18T04:10:24.930729Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd17d336dc746a99c57c6b6cb65e643c6f9414006ee777155d47a9017b6d6598

Aliases

arxiv: 1110.5005 · arxiv_version: 1110.5005v1 · doi: 10.48550/arxiv.1110.5005 · pith_short_12: XUL5GNW4ORVJ · pith_short_16: XUL5GNW4ORVJTRL4 · pith_short_8: XUL5GNW4

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/XUL5GNW4ORVJTRL4NNWLMXTEHR \
  | 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: bd17d336dc746a99c57c6b6cb65e643c6f9414006ee777155d47a9017b6d6598

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "062fc9547610b4c9bf80f0d7bd54ebf331d3aaeb66a26b1b9b6cda4960394e82",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-10-22T22:22:51Z",
    "title_canon_sha256": "82d12456063a561a478a37ec0c0605f6200e595d2050925449d7b937667e511d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5005",
    "kind": "arxiv",
    "version": 1
  }
}