Pith Number

pith:Z2AF5Z7U

pith:2016:Z2AF5Z7U6VEOR6FAILBUCBU2ZE

not attested not anchored not stored refs pending

Factoring groups into dense subsets

Igor Protasov, Serhii Slobodianiuk

arxiv:1602.01603 v1 · 2016-02-04 · 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{Z2AF5Z7U6VEOR6FAILBUCBU2ZE}

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	2026-05-18T01:21:18.567383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce805ee7f4f548e8f8a042c341069ac9125dce77694f171affa6745f37c48b5c

Aliases

arxiv: 1602.01603 · arxiv_version: 1602.01603v1 · doi: 10.48550/arxiv.1602.01603 · pith_short_12: Z2AF5Z7U6VEO · pith_short_16: Z2AF5Z7U6VEOR6FA · pith_short_8: Z2AF5Z7U

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/Z2AF5Z7U6VEOR6FAILBUCBU2ZE \
  | 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: ce805ee7f4f548e8f8a042c341069ac9125dce77694f171affa6745f37c48b5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c0f439aa6830b8047fd80aaa74e6e8eb7f75f3dd2a085d6974d77d6ac8f2bd8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-02-04T09:34:02Z",
    "title_canon_sha256": "032ce213c9bc5572821f8dbb75a9b27df2e74ee1931f28a25fe4d6361a4032c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.01603",
    "kind": "arxiv",
    "version": 1
  }
}