Pith Number

pith:QZWQEA24

pith:2013:QZWQEA24WTFHEQ42G7QAAMAF5G

not attested not anchored not stored refs pending

Non-hyperbolic automatic groups and groups acting on CAT(0) cube complex

Makoto Tamura, Yasushi Yamashita, Yoshiyuki Nakagawa

arxiv:1309.5553 v1 · 2013-09-22 · 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{QZWQEA24WTFHEQ42G7QAAMAF5G}

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	2026-05-18T02:42:06.147939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

866d02035cb4ca72439a37e0003005e9b739e6447812e25395142c1d21374739

Aliases

arxiv: 1309.5553 · arxiv_version: 1309.5553v1 · doi: 10.48550/arxiv.1309.5553 · pith_short_12: QZWQEA24WTFH · pith_short_16: QZWQEA24WTFHEQ42 · pith_short_8: QZWQEA24

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/QZWQEA24WTFHEQ42G7QAAMAF5G \
  | 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: 866d02035cb4ca72439a37e0003005e9b739e6447812e25395142c1d21374739

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ccadf74a9eca8b945c95077b2d0e7e8067c272a68d3e58805620b4f8d272cd88",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-22T02:48:21Z",
    "title_canon_sha256": "20fbd81b32f67e57b22df792d40ea90bff013a3d84d73f65328944284cb0551e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.5553",
    "kind": "arxiv",
    "version": 1
  }
}