Pith Number

pith:RK7FKRJL

pith:2011:RK7FKRJLGSE2H42WOTLJUU2MO2

not attested not anchored not stored refs pending

Kurosh rank of intersections of subgroups of free products of orderable groups

Armando Martino, Inga Schwabrow, Yago Antol\'in

arxiv:1109.0233 v3 · 2011-09-01 · 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{RK7FKRJLGSE2H42WOTLJUU2MO2}

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	2026-05-18T03:01:33.611251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8abe55452b3489a3f35674d69a534c7689e2e869f6af2326d6125ef850bf7b56

Aliases

arxiv: 1109.0233 · arxiv_version: 1109.0233v3 · doi: 10.48550/arxiv.1109.0233 · pith_short_12: RK7FKRJLGSE2 · pith_short_16: RK7FKRJLGSE2H42W · pith_short_8: RK7FKRJL

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/RK7FKRJLGSE2H42WOTLJUU2MO2 \
  | 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: 8abe55452b3489a3f35674d69a534c7689e2e869f6af2326d6125ef850bf7b56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04425c8cffe9f90068b3529480b48c2a524bdc1292f847dce9133704f03c9657",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-09-01T16:50:51Z",
    "title_canon_sha256": "ed30cb070464595db2c96ff0ab2326f5227624660a55710f195ec15c20a636c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0233",
    "kind": "arxiv",
    "version": 3
  }
}