Pith Number

pith:KL3PK5OK

pith:2015:KL3PK5OKINQ4XNY3SUIXAP7UKU

not attested not anchored not stored refs pending

Minimality of the Semidirect Product

Luie Polev, Menachem Shlossberg, Michael Megrelishvili

arxiv:1511.07021 v3 · 2015-11-22 · math.GN · 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{KL3PK5OKINQ4XNY3SUIXAP7UKU}

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	2026-05-18T01:01:09.543831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52f6f575ca4361cbb71b9511703ff4553d9c63b58ef83d033f2cb83a8b91b99e

Aliases

arxiv: 1511.07021 · arxiv_version: 1511.07021v3 · doi: 10.48550/arxiv.1511.07021 · pith_short_12: KL3PK5OKINQ4 · pith_short_16: KL3PK5OKINQ4XNY3 · pith_short_8: KL3PK5OK

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/KL3PK5OKINQ4XNY3SUIXAP7UKU \
  | 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: 52f6f575ca4361cbb71b9511703ff4553d9c63b58ef83d033f2cb83a8b91b99e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c571246a82a07788fedb298d5e2d27c84c4090548c1a5bddbc716f1615774b00",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2015-11-22T15:12:03Z",
    "title_canon_sha256": "cac14407b38a07116065be72b0a5141b5fd8a0eb7df8af43d52bd5ee286a6bfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07021",
    "kind": "arxiv",
    "version": 3
  }
}