Pith Number

pith:HMYP4CKC

pith:2013:HMYP4CKCOLBB6U46GJWJOKGKVG

not attested not anchored not stored refs pending

The Minimum Number of Hubs in Networks

Easton Li Xu, Guangyue Han

arxiv:1308.2865 v1 · 2013-08-13 · 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{HMYP4CKCOLBB6U46GJWJOKGKVG}

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	2026-05-18T03:15:58.321308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b30fe094272c21f539e326c9728caa98a358f984cf050eba9f9a4ce2eea0ae8

Aliases

arxiv: 1308.2865 · arxiv_version: 1308.2865v1 · doi: 10.48550/arxiv.1308.2865 · pith_short_12: HMYP4CKCOLBB · pith_short_16: HMYP4CKCOLBB6U46 · pith_short_8: HMYP4CKC

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/HMYP4CKCOLBB6U46GJWJOKGKVG \
  | 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: 3b30fe094272c21f539e326c9728caa98a358f984cf050eba9f9a4ce2eea0ae8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc8fbe9aac8fd5b95296e18cb93e7f0a52e4d12c649ac41696b506475e7b9aa8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-08-13T13:41:57Z",
    "title_canon_sha256": "2ebb9457f146d1497ff6d047a98f533deacf0141cfd3993b236bd3fecaf82822"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2865",
    "kind": "arxiv",
    "version": 1
  }
}