Pith Number

pith:5SGM62Z4

pith:2015:5SGM62Z4PFU4NNRBQAFMVNPJYH

not attested not anchored not stored refs pending

Ramanujan Cayley graphs of Frobenius groups

Kohei Katata, Miki Hirano, Yoshinori Yamasaki

arxiv:1503.04075 v1 · 2015-03-13 · math.NT · 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{5SGM62Z4PFU4NNRBQAFMVNPJYH}

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	2026-05-18T00:15:31.316562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec8ccf6b3c7969c6b621800acab5e9c1c65c75a8183ce6c526be97ee9aef4ec1

Aliases

arxiv: 1503.04075 · arxiv_version: 1503.04075v1 · doi: 10.48550/arxiv.1503.04075 · pith_short_12: 5SGM62Z4PFU4 · pith_short_16: 5SGM62Z4PFU4NNRB · pith_short_8: 5SGM62Z4

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/5SGM62Z4PFU4NNRBQAFMVNPJYH \
  | 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: ec8ccf6b3c7969c6b621800acab5e9c1c65c75a8183ce6c526be97ee9aef4ec1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1c81754572b36fbbecb84b9e04403b9330222d1224694d2448cf98447cb00ac",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-03-13T14:10:41Z",
    "title_canon_sha256": "8a44e6f7430086eb93d06ef8e8c2fb1d891989bb35483e4ec0294c379a9935bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04075",
    "kind": "arxiv",
    "version": 1
  }
}