Pith Number

pith:YPZI5YT5

pith:2013:YPZI5YT5EJ2KA7TXURTLIWS6VF

not attested not anchored not stored refs pending

On abelian subgroups of finitely generated metabelian groups

Alexander Yu. Olshanskii, Vahagn H. Mikaelian

arxiv:1302.2272 v2 · 2013-02-09 · 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{YPZI5YT5EJ2KA7TXURTLIWS6VF}

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	2026-05-18T03:10:37.061177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3f28ee27d2274a07e77a466b45a5ea972cf5266a0b337cdef1902170f01bb01

Aliases

arxiv: 1302.2272 · arxiv_version: 1302.2272v2 · doi: 10.48550/arxiv.1302.2272 · pith_short_12: YPZI5YT5EJ2K · pith_short_16: YPZI5YT5EJ2KA7TX · pith_short_8: YPZI5YT5

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/YPZI5YT5EJ2KA7TXURTLIWS6VF \
  | 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: c3f28ee27d2274a07e77a466b45a5ea972cf5266a0b337cdef1902170f01bb01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7b0ba826069ec83e85869654a43fbb314f298316dde7d91f776feffb184cd34",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-02-09T21:26:11Z",
    "title_canon_sha256": "befae222c214436b64cf6b9f7a8232fca2a25794db42a6faf5b574c234ea9702"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.2272",
    "kind": "arxiv",
    "version": 2
  }
}