Pith Number

pith:JTSP5A4P

pith:2010:JTSP5A4PTNFG26LT3Y7KLOB4YA

not attested not anchored not stored refs pending

An Outer Commutator Multiplier and Capability of Finitely Generated Abelian Groups

Behrooz Mashayekhy, Mohsen Parvizi

arxiv:1012.3244 v1 · 2010-12-15 · 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{JTSP5A4PTNFG26LT3Y7KLOB4YA}

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	2026-05-18T01:26:03.329427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ce4fe838f9b4a6d7973de3ea5b83cc025a2c7b00bd3e4da8d47f318387758dc

Aliases

arxiv: 1012.3244 · arxiv_version: 1012.3244v1 · doi: 10.48550/arxiv.1012.3244 · pith_short_12: JTSP5A4PTNFG · pith_short_16: JTSP5A4PTNFG26LT · pith_short_8: JTSP5A4P

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/JTSP5A4PTNFG26LT3Y7KLOB4YA \
  | 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: 4ce4fe838f9b4a6d7973de3ea5b83cc025a2c7b00bd3e4da8d47f318387758dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21ad7c3efbeb419ee5b94660566ef099627ef304d8096d6bc0216bb8ce4e4123",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-15T08:22:34Z",
    "title_canon_sha256": "1b403399f0fdb40f6dea3366e2dd88026e3e9ed10af806876c450900d7c4dade"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3244",
    "kind": "arxiv",
    "version": 1
  }
}