Pith Number

pith:3CIORN5V

pith:2026:3CIORN5VZJFK44AAZMHUV3RKDF

not attested not anchored not stored refs pending

Maximizing the algebraic connectivity of graphs of given order and size: a proof of a conjecture of Kolokolnikov

Abhay Jayarajan, M. Rajesh Kannan, Rahul Roy, Sebastian M. Cioab\u{a}

arxiv:2608.09879 v1 · 2026-08-10 · 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{3CIORN5VZJFK44AAZMHUV3RKDF}

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	2026-08-11T02:25:19.432041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d890e8b7b5ca4aae7000cb0f4aee2a1941dff233d786db32792e11983b7d42b2

Aliases

arxiv: 2608.09879 · arxiv_version: 2608.09879v1 · doi: 10.48550/arxiv.2608.09879 · pith_short_12: 3CIORN5VZJFK · pith_short_16: 3CIORN5VZJFK44AA · pith_short_8: 3CIORN5V

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/3CIORN5VZJFK44AAZMHUV3RKDF \
  | 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: d890e8b7b5ca4aae7000cb0f4aee2a1941dff233d786db32792e11983b7d42b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e5039f7e036e72369f23984c2e3519c9bee61e244ae940c3e7254eef21c21d9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-10T17:32:53Z",
    "title_canon_sha256": "83ca1c35a8b096c7307c246c1b5207d91a32ef61cf5f4fa238d991500c5395dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09879",
    "kind": "arxiv",
    "version": 1
  }
}