Pith Number

pith:3QTJPMBL

pith:2012:3QTJPMBLCF64YQZ2QMDNKIAPNC

not attested not anchored not stored refs pending

Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian

Dave Witte Morris

arxiv:1205.0087 v1 · 2012-05-01 · 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{3QTJPMBLCF64YQZ2QMDNKIAPNC}

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	2026-05-18T03:56:35.895373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc2697b02b117dcc433a8306d5200f68a0aadd2d212c49a6d7c27f7d26404e63

Aliases

arxiv: 1205.0087 · arxiv_version: 1205.0087v1 · doi: 10.48550/arxiv.1205.0087 · pith_short_12: 3QTJPMBLCF64 · pith_short_16: 3QTJPMBLCF64YQZ2 · pith_short_8: 3QTJPMBL

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/3QTJPMBLCF64YQZ2QMDNKIAPNC \
  | 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: dc2697b02b117dcc433a8306d5200f68a0aadd2d212c49a6d7c27f7d26404e63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc9beea7a8a7e0caa8db14bb0c20cef14111aed39304eb6384484dd47f0a90f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-01T04:48:16Z",
    "title_canon_sha256": "22961030b4be406ec751d7cdfeb9043d3b4dc2b362375c4024da491cf2fa6bd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.0087",
    "kind": "arxiv",
    "version": 1
  }
}