Pith Number

pith:3JWCCFR6

pith:2014:3JWCCFR6ZDPUFDLHN7M6MK4M32

not attested not anchored not stored refs pending

Graphs of order $n$ and diameter $2(n-1)/3$ minimizing the spectral radius

Jingfen Lan, Lingsheng Shi

arxiv:1405.5015 v1 · 2014-05-20 · math.SP · 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{3JWCCFR6ZDPUFDLHN7M6MK4M32}

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	2026-05-18T02:51:32.352277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da6c21163ec8df428d676fd9e62b8cde88f23189cddd8edab1d82d84a56f3bf3

Aliases

arxiv: 1405.5015 · arxiv_version: 1405.5015v1 · doi: 10.48550/arxiv.1405.5015 · pith_short_12: 3JWCCFR6ZDPU · pith_short_16: 3JWCCFR6ZDPUFDLH · pith_short_8: 3JWCCFR6

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/3JWCCFR6ZDPUFDLHN7M6MK4M32 \
  | 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: da6c21163ec8df428d676fd9e62b8cde88f23189cddd8edab1d82d84a56f3bf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "818cb19a7f8991b33d78222ccf849b2edc53b618da62dd81d4bd6d2e592e3e99",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2014-05-20T09:54:59Z",
    "title_canon_sha256": "e46252cf5357a91ba00ceb9dff1dc32c3f47f14b71f6a161c092741b4759a4a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.5015",
    "kind": "arxiv",
    "version": 1
  }
}