Pith Number

pith:N3FBX4MC

pith:2026:N3FBX4MC65X3MC4TQYN5GA77MO

not attested not anchored not stored refs pending

Multiplicity of Laplacian eigenvalue 1 of a graph

Fenglei Tian, Yuhao Zhou

arxiv:2606.11547 v1 · 2026-06-10 · 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{N3FBX4MC65X3MC4TQYN5GA77MO}

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	2026-06-11T01:09:55.443795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6eca1bf182f76fb60b93861bd303ff639463dcd4b50aa0bf3cd7233881a64cfc

Aliases

arxiv: 2606.11547 · arxiv_version: 2606.11547v1 · doi: 10.48550/arxiv.2606.11547 · pith_short_12: N3FBX4MC65X3 · pith_short_16: N3FBX4MC65X3MC4T · pith_short_8: N3FBX4MC

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/N3FBX4MC65X3MC4TQYN5GA77MO \
  | 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: 6eca1bf182f76fb60b93861bd303ff639463dcd4b50aa0bf3cd7233881a64cfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a11bd7477c89388f90155826a45a4a1f99732be19354b23261106cac2cb278f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-10T01:14:07Z",
    "title_canon_sha256": "1f9826f278e089dd676fcd57cc800271123ab7f1c8637857a72496b5c105d201"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11547",
    "kind": "arxiv",
    "version": 1
  }
}