Pith Number

pith:Z6BGF5JB

pith:2013:Z6BGF5JBBGMBSQDUKR2AVXTNOP

not attested not anchored not stored refs pending

Quadratic Equations in Hyperbolic Groups are NP-complete

Alex Taam, Alina Vdovina, Atefeh Mohajeri, Olga Kharlampovich

arxiv:1306.0941 v4 · 2013-06-04 · 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{Z6BGF5JBBGMBSQDUKR2AVXTNOP}

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	2026-05-18T00:08:05.570161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf8262f521099819407454740ade6d73eaec9280ae37437e08ea54fdb961c4cd

Aliases

arxiv: 1306.0941 · arxiv_version: 1306.0941v4 · doi: 10.48550/arxiv.1306.0941 · pith_short_12: Z6BGF5JBBGMB · pith_short_16: Z6BGF5JBBGMBSQDU · pith_short_8: Z6BGF5JB

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/Z6BGF5JBBGMBSQDUKR2AVXTNOP \
  | 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: cf8262f521099819407454740ade6d73eaec9280ae37437e08ea54fdb961c4cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7aee6b2e82e682d35403260b5861d78b65200afa31eb4da618d7ce808d8c0da0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-06-04T23:14:29Z",
    "title_canon_sha256": "c97ddc6a51def3e462ce2d8e298888ede55de12701552612d6bdee5e83883e33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0941",
    "kind": "arxiv",
    "version": 4
  }
}