Pith Number

pith:ZEBSN3FK

pith:2013:ZEBSN3FKD5KPBQGPYV4OAQXABI

not attested not anchored not stored refs pending

On $\Pi$-supplemented subgroups of a finite group

Wenbin Guo, Xiaoyu Chen

arxiv:1307.0089 v4 · 2013-06-29 · 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{ZEBSN3FKD5KPBQGPYV4OAQXABI}

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	2026-05-18T03:03:09.942768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c90326ecaa1f54f0c0cfc578e042e00a0ac221c8ca3931f453f9735a25ef41dd

Aliases

arxiv: 1307.0089 · arxiv_version: 1307.0089v4 · doi: 10.48550/arxiv.1307.0089 · pith_short_12: ZEBSN3FKD5KP · pith_short_16: ZEBSN3FKD5KPBQGP · pith_short_8: ZEBSN3FK

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/ZEBSN3FKD5KPBQGPYV4OAQXABI \
  | 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: c90326ecaa1f54f0c0cfc578e042e00a0ac221c8ca3931f453f9735a25ef41dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d11b4ee1bfa3206d9c2551cef7d1980598d0eff7e21196b6db96d192ec4772e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-06-29T11:16:20Z",
    "title_canon_sha256": "ea882246ea5339a17b48a1b3752589636b09fcd907078aa098372e150435f591"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0089",
    "kind": "arxiv",
    "version": 4
  }
}