Pith Number

pith:3MQQQL4N

pith:2016:3MQQQL4N6OHUHK3MGRBHJTFDBG

not attested not anchored not stored refs pending

kirchhoff index and degree kirchhoff index of complete multipartite graph

Jia-Bao Liu, Masoud Karimi, Ravindra B. Bapat

arxiv:1611.09457 v1 · 2016-11-29 · 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{3MQQQL4N6OHUHK3MGRBHJTFDBG}

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	2026-05-18T00:56:18.479856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db21082f8df38f43ab6c344274cca3098e0ba104389080dcfe707ae34703cca4

Aliases

arxiv: 1611.09457 · arxiv_version: 1611.09457v1 · doi: 10.48550/arxiv.1611.09457 · pith_short_12: 3MQQQL4N6OHU · pith_short_16: 3MQQQL4N6OHUHK3M · pith_short_8: 3MQQQL4N

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/3MQQQL4N6OHUHK3MGRBHJTFDBG \
  | 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: db21082f8df38f43ab6c344274cca3098e0ba104389080dcfe707ae34703cca4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fbdf51969d65dbef8309650711ef704c67cf25ef422415a37e69ebb6be59702",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-11-29T02:13:03Z",
    "title_canon_sha256": "4fd3a11fedf6d0bae8c46abfd980690459b66f39dc63d8924784009ed93d5baf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09457",
    "kind": "arxiv",
    "version": 1
  }
}