Pith Number

pith:Z3TPPBQK

pith:2011:Z3TPPBQKHMT4OXZFJBOKF5KEAY

not attested not anchored not stored refs pending

JSJ decompositions of Quadratic Baumslag-Solitar groups

Juan Alonso

arxiv:1102.4589 v3 · 2011-02-22 · 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{Z3TPPBQKHMT4OXZFJBOKF5KEAY}

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	2026-05-18T01:22:29.104131Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cee6f7860a3b27c75f25485ca2f5440632948f0011e38c93da2c28f6f6a6da84

Aliases

arxiv: 1102.4589 · arxiv_version: 1102.4589v3 · doi: 10.48550/arxiv.1102.4589 · pith_short_12: Z3TPPBQKHMT4 · pith_short_16: Z3TPPBQKHMT4OXZF · pith_short_8: Z3TPPBQK

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/Z3TPPBQKHMT4OXZFJBOKF5KEAY \
  | 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: cee6f7860a3b27c75f25485ca2f5440632948f0011e38c93da2c28f6f6a6da84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2898a87d50639a0c6b73e9702841e53d68f4e8cd2e6d7bac49024e2a16aef34e",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-02-22T19:33:12Z",
    "title_canon_sha256": "1fc95b8a4b18b5ea5a00e81dfcc5bd00a1dd37203362fb497a96c5ad6df0c01d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4589",
    "kind": "arxiv",
    "version": 3
  }
}