Pith Number

pith:3V2JZ2J6

pith:2016:3V2JZ2J63RFU3VJOMMMDF32QOK

not attested not anchored not stored refs pending

On the power graph of the direct product of two groups

A. K. Bhuniya, Sajal Kumar Mukherjee

arxiv:1606.07258 v1 · 2016-06-23 · math.CO · 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{3V2JZ2J63RFU3VJOMMMDF32QOK}

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	2026-05-18T01:11:58.356577Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd749ce93edc4b4dd52e631832ef50729104c34f7ef1a4ad6835fc89207d78f4

Aliases

arxiv: 1606.07258 · arxiv_version: 1606.07258v1 · doi: 10.48550/arxiv.1606.07258 · pith_short_12: 3V2JZ2J63RFU · pith_short_16: 3V2JZ2J63RFU3VJO · pith_short_8: 3V2JZ2J6

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/3V2JZ2J63RFU3VJOMMMDF32QOK \
  | 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: dd749ce93edc4b4dd52e631832ef50729104c34f7ef1a4ad6835fc89207d78f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ad8401dc469c0d3e58e06552483d8b29a58c38ff2cdb535383bc951222de471",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-23T10:20:34Z",
    "title_canon_sha256": "631446481f7603f55a3abef5935b79f3b386fdaa30a74cee9027c7fddcfaa8eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.07258",
    "kind": "arxiv",
    "version": 1
  }
}