Pith Number

pith:CXQM324I

pith:2025:CXQM324I33RHVQFBRAUQWFGKER

not attested not anchored not stored refs pending

Perfect codes in Cayley graphs of abelian groups

Peter J. Cameron, Roro Sihui Yap, Sanming Zhou

arxiv:2507.11871 v2 · 2025-07-16 · 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{CXQM324I33RHVQFBRAUQWFGKER}

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	2026-05-20T00:02:52.033758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15e0cdeb88dee27ac0a188290b14ca2458d70d1c7dc9c52f732f3f22a9bf9a82

Aliases

arxiv: 2507.11871 · arxiv_version: 2507.11871v2 · doi: 10.48550/arxiv.2507.11871 · pith_short_12: CXQM324I33RH · pith_short_16: CXQM324I33RHVQFB · pith_short_8: CXQM324I

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/CXQM324I33RHVQFBRAUQWFGKER \
  | 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: 15e0cdeb88dee27ac0a188290b14ca2458d70d1c7dc9c52f732f3f22a9bf9a82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c145dfb60bcf13f4d8134c8be0ad26de8468c642d08f530c01a2327c7ab70274",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-16T03:34:24Z",
    "title_canon_sha256": "0fd0d6536f03b168bbbca37090552427ead33ec6d8e709f4b6e25b6208286b26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.11871",
    "kind": "arxiv",
    "version": 2
  }
}