Pith Number

pith:TIBH3TIW

pith:2011:TIBH3TIWDAJBSTUVLPLQ3YSW2F

not attested not anchored not stored refs pending

Graphs with Diameter $n-e$ Minimizing the Spectral Radius

Jingfen Lan, Lingsheng Shi, Linyuan Lu

arxiv:1110.2444 v1 · 2011-10-11 · 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{TIBH3TIWDAJBSTUVLPLQ3YSW2F}

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	2026-05-18T04:11:09.027370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a027dcd161812194e955bd70de256d14e29f198e0c113e29e8feef02f74eb0c

Aliases

arxiv: 1110.2444 · arxiv_version: 1110.2444v1 · doi: 10.48550/arxiv.1110.2444 · pith_short_12: TIBH3TIWDAJB · pith_short_16: TIBH3TIWDAJBSTUV · pith_short_8: TIBH3TIW

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/TIBH3TIWDAJBSTUVLPLQ3YSW2F \
  | 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: 9a027dcd161812194e955bd70de256d14e29f198e0c113e29e8feef02f74eb0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdeb29759fbcb4480c098fea83050ce74902d75f9d4bd29402b21b6757aea8aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-10-11T17:30:09Z",
    "title_canon_sha256": "e31fb2558f70a66dc6840503d2321c0f9c1af1ed5174272fa2a83728b3d36910"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2444",
    "kind": "arxiv",
    "version": 1
  }
}