Pith Number

pith:ISKMPYPS

pith:2013:ISKMPYPSYQTPNYG3QZUPVDC4B4

not attested not anchored not stored refs pending

Characterizing the second smallest eigenvalue of the normalized Laplacian of a tree

Israel Rocha

arxiv:1306.2374 v1 · 2013-06-10 · 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{ISKMPYPSYQTPNYG3QZUPVDC4B4}

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	2026-05-18T03:21:21.203622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4494c7e1f2c426f6e0db8668fa8c5c0f3a1313176567b53cc4783f7581dbb15c

Aliases

arxiv: 1306.2374 · arxiv_version: 1306.2374v1 · doi: 10.48550/arxiv.1306.2374 · pith_short_12: ISKMPYPSYQTP · pith_short_16: ISKMPYPSYQTPNYG3 · pith_short_8: ISKMPYPS

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/ISKMPYPSYQTPNYG3QZUPVDC4B4 \
  | 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: 4494c7e1f2c426f6e0db8668fa8c5c0f3a1313176567b53cc4783f7581dbb15c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1eb8b5159017dbafbf4a66b98c0a15d1175fa00085b9e0faf8d0014bc132087",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-10T22:38:35Z",
    "title_canon_sha256": "f913f00e8a3377d4d840ca46f4136410ad41e562d4b3063367f3ed9437f76615"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2374",
    "kind": "arxiv",
    "version": 1
  }
}