Pith Number

pith:7F7HKW23

pith:2017:7F7HKW23WU6UKJKR2ID5KNFIJY

not attested not anchored not stored refs pending

Quasiperiodic and mixed commutator factorizations in free products of groups

Anton A. Klyachko, S. V. Ivanov

arxiv:1702.01379 v3 · 2017-02-05 · 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{7F7HKW23WU6UKJKR2ID5KNFIJY}

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	2026-05-18T00:04:24.196746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f97e755b5bb53d452551d207d534a84e2c85a0471bb89b668c7f0d6891c37faf

Aliases

arxiv: 1702.01379 · arxiv_version: 1702.01379v3 · doi: 10.48550/arxiv.1702.01379 · pith_short_12: 7F7HKW23WU6U · pith_short_16: 7F7HKW23WU6UKJKR · pith_short_8: 7F7HKW23

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/7F7HKW23WU6UKJKR2ID5KNFIJY \
  | 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: f97e755b5bb53d452551d207d534a84e2c85a0471bb89b668c7f0d6891c37faf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7e80442c0d4c6cb831b3267a708b42da53af7f42db0e216d112beb0d9bb7a60",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-02-05T07:55:55Z",
    "title_canon_sha256": "b7ddefeb5c2c255ead7daa5618ac75d6d3a19df12b9ebdd08833086c41cb650b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.01379",
    "kind": "arxiv",
    "version": 3
  }
}