Pith Number

pith:73CTCITP

pith:2012:73CTCITPQB3S66XPRVYQ5OJGMQ

not attested not anchored not stored refs pending

Some Characterizations of a Normal Subgroup of a Group

R. P. Shukla, Vipul Kakkar

arxiv:1202.5626 v2 · 2012-02-25 · 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{73CTCITPQB3S66XPRVYQ5OJGMQ}

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	2026-05-18T04:00:26.301433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fec531226f80772f7aef8d710eb926641f908bed66d54ed2b3a36d9e38a37b58

Aliases

arxiv: 1202.5626 · arxiv_version: 1202.5626v2 · doi: 10.48550/arxiv.1202.5626 · pith_short_12: 73CTCITPQB3S · pith_short_16: 73CTCITPQB3S66XP · pith_short_8: 73CTCITP

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/73CTCITPQB3S66XPRVYQ5OJGMQ \
  | 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: fec531226f80772f7aef8d710eb926641f908bed66d54ed2b3a36d9e38a37b58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1156b72e29d7cafcd1c938fc3344e51826de37fd59483be214de69a89966ad8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-02-25T08:01:32Z",
    "title_canon_sha256": "b61602d95994330e3b22075a1745443a9266d58b59756da20e36cb0783f68fff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5626",
    "kind": "arxiv",
    "version": 2
  }
}