Pith Number

pith:YP7YNKG3

pith:2013:YP7YNKG3DNXIC2HIWNAZYU6RY4

not attested not anchored not stored refs pending

Cross Number Invariants of Finite Abelian Groups

Xiaoyu He

arxiv:1308.3896 v2 · 2013-08-18 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YP7YNKG3DNXIC2HIWNAZYU6RY4}

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	2026-05-18T00:40:08.782049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3ff86a8db1b6e8168e8b3419c53d1c729fc6954185b44c3aaebc9a4dbf5214c

Aliases

arxiv: 1308.3896 · arxiv_version: 1308.3896v2 · doi: 10.48550/arxiv.1308.3896 · pith_short_12: YP7YNKG3DNXI · pith_short_16: YP7YNKG3DNXIC2HI · pith_short_8: YP7YNKG3

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/YP7YNKG3DNXIC2HIWNAZYU6RY4 \
  | 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: c3ff86a8db1b6e8168e8b3419c53d1c729fc6954185b44c3aaebc9a4dbf5214c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e671c93117441cfaffd1dea61aff6b6086ed7c56ba5e2dbd223ea2ed42152ad0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-08-18T21:38:56Z",
    "title_canon_sha256": "6c7e4837fea17bf0bacc4ea9bd8e59c0519d861efc16056304251a234866727c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3896",
    "kind": "arxiv",
    "version": 2
  }
}