Pith Number

pith:7LSHXZUE

pith:2012:7LSHXZUE55YKRYDE5RI5AJEP7A

not attested not anchored not stored refs pending

A parabolic action on a proper, CAT(0) cube complex

Bronislaw Wajnryb, Pawel Witowicz, Yael Algom-Kfir

arxiv:1209.5804 v2 · 2012-09-26 · 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{7LSHXZUE55YKRYDE5RI5AJEP7A}

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	2026-05-18T03:44:23.546613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fae47be684ef70a8e064ec51d0248ff83eeb6c3be60f6b29ad88b8c2d96774f3

Aliases

arxiv: 1209.5804 · arxiv_version: 1209.5804v2 · doi: 10.48550/arxiv.1209.5804 · pith_short_12: 7LSHXZUE55YK · pith_short_16: 7LSHXZUE55YKRYDE · pith_short_8: 7LSHXZUE

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/7LSHXZUE55YKRYDE5RI5AJEP7A \
  | 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: fae47be684ef70a8e064ec51d0248ff83eeb6c3be60f6b29ad88b8c2d96774f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a3c1e83424eabf21e91fd269e6c15d62bf17d670d4a8fb2adbd85b15aad2280",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-09-26T01:15:24Z",
    "title_canon_sha256": "863fae818e8c9cabd0e5d7c02046c4e45ef2cdb3a5da075d65cea35d377b2a0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5804",
    "kind": "arxiv",
    "version": 2
  }
}