Pith Number

pith:3NSKYB3H

pith:2012:3NSKYB3H5B76MGLXUBJXVJD632

not attested not anchored not stored refs pending

A few properties of the eigenvalues of normalized graph Laplacian

Anirban Banerjee

arxiv:1210.5091 v2 · 2012-10-18 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NSKYB3H5B76MGLXUBJXVJD632}

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	2026-05-18T02:57:00.128253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db64ac0767e87fe61977a0537aa47edea7693e36558fadeac5e55e1bc5c7e882

Aliases

arxiv: 1210.5091 · arxiv_version: 1210.5091v2 · doi: 10.48550/arxiv.1210.5091 · pith_short_12: 3NSKYB3H5B76 · pith_short_16: 3NSKYB3H5B76MGLX · pith_short_8: 3NSKYB3H

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/3NSKYB3H5B76MGLXUBJXVJD632 \
  | 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: db64ac0767e87fe61977a0537aa47edea7693e36558fadeac5e55e1bc5c7e882

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d69ea84d2ad6180bbd72edf47f7a105bd158f91d5c68c71065089887b37667f",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-18T11:12:43Z",
    "title_canon_sha256": "727b74f54a98464779bdd4c68c28a4c50711fa3c659ca7f0507a6f4f1e66e994"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5091",
    "kind": "arxiv",
    "version": 2
  }
}