Pith Number

pith:4CZD6SI2

pith:2015:4CZD6SI22POTAA4C35XDNWW73M

not attested not anchored not stored refs pending

Constructive and analytic enumeration of circulant graphs with $p^3$ vertices; $p=3,5$

Josef Lauri, Mikhail Klin, Valery Liskovets, Victoria Gatt

arxiv:1512.07744 v4 · 2015-12-24 · 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{4CZD6SI22POTAA4C35XDNWW73M}

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	2026-05-18T00:19:04.679755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0b23f491ad3dd300382df6e36dadfdb3b34ee6f33bbc3a1cede4edc340654b0

Aliases

arxiv: 1512.07744 · arxiv_version: 1512.07744v4 · doi: 10.48550/arxiv.1512.07744 · pith_short_12: 4CZD6SI22POT · pith_short_16: 4CZD6SI22POTAA4C · pith_short_8: 4CZD6SI2

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/4CZD6SI22POTAA4C35XDNWW73M \
  | 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: e0b23f491ad3dd300382df6e36dadfdb3b34ee6f33bbc3a1cede4edc340654b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8515c2c6eb1f49e8458654521e14625c69cd839c39498c1d9619d96095d3d2e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-24T08:09:00Z",
    "title_canon_sha256": "290d88aaea9d3c2deca583617ef2d861ab0bfd5fff63f23cc469ec9b5b8e645e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07744",
    "kind": "arxiv",
    "version": 4
  }
}