Pith Number

pith:XH53KPIW

pith:2017:XH53KPIW47VBI5FONANANL4JEI

not attested not anchored not stored refs pending

Balanced and functionally balanced $P$-groups

Menachem Shlossberg

arxiv:1707.09027 v1 · 2017-07-27 · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XH53KPIW47VBI5FONANANL4JEI}

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	2026-05-18T00:39:17.331230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9fbb53d16e7ea1474ae681a06af89222e4d25ada630f79fd0873e3899178d22

Aliases

arxiv: 1707.09027 · arxiv_version: 1707.09027v1 · doi: 10.48550/arxiv.1707.09027 · pith_short_12: XH53KPIW47VB · pith_short_16: XH53KPIW47VBI5FO · pith_short_8: XH53KPIW

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/XH53KPIW47VBI5FONANANL4JEI \
  | 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: b9fbb53d16e7ea1474ae681a06af89222e4d25ada630f79fd0873e3899178d22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "275d842dd0fab5d3cbd5b077a5c2d5b6bc2ceaa3b10efdf96ad1eef3daa96c15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2017-07-27T19:57:21Z",
    "title_canon_sha256": "d247ce056246696189201799190298ece09a173e2c44ec12302880f9385180d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.09027",
    "kind": "arxiv",
    "version": 1
  }
}