Pith Number

pith:KTGQ3ZYN

pith:2012:KTGQ3ZYNFYMQF4JYC7YJQOMCYH

not attested not anchored not stored refs pending

Representing and counting the subgroups of the group Z_m x Z_n

Christoph Wiesmeyr, L\'aszl\'o T\'oth, Mario Hampejs, Nicki Holighaus

arxiv:1211.1797 v3 · 2012-11-08 · math.GR · math.CO · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KTGQ3ZYNFYMQF4JYC7YJQOMCYH}

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.

Cited by

1 paper in Pith

Recovery of Integer Images from Minimal DFT Measurements: Uniqueness and Inversion Algorithms

Receipt and verification

First computed	2026-05-18T02:39:24.273373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54cd0de70d2e1902f13817f0983982c1c80275470d06300ab439795acd17a411

Aliases

arxiv: 1211.1797 · arxiv_version: 1211.1797v3 · doi: 10.48550/arxiv.1211.1797 · pith_short_12: KTGQ3ZYNFYMQ · pith_short_16: KTGQ3ZYNFYMQF4JY · pith_short_8: KTGQ3ZYN

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/KTGQ3ZYNFYMQF4JYC7YJQOMCYH \
  | 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: 54cd0de70d2e1902f13817f0983982c1c80275470d06300ab439795acd17a411

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8b6acab6430e67b9b0a8291a2e7f7b9c843d65ff26fc70903b38d20f6728c0c",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-08T09:19:31Z",
    "title_canon_sha256": "2c48c290510af569e736de71deab9103db90e428cc2693e2a66eb008de656ff8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1797",
    "kind": "arxiv",
    "version": 3
  }
}