Pith Number

pith:6MSS5EZI

pith:2011:6MSS5EZIJ2JZBWBQI3VLHPH2FO

not attested not anchored not stored refs pending

On sum of powers of Laplacian eigenvalues and Laplacian Estrada index of graphs

Bo Zhou

arxiv:1102.1144 v1 · 2011-02-06 · 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{6MSS5EZIJ2JZBWBQI3VLHPH2FO}

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	2026-05-18T04:29:54.933370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3252e93284e9390d83046eab3bcfa2ba08a69727f37cf90f5de8af2e403df06

Aliases

arxiv: 1102.1144 · arxiv_version: 1102.1144v1 · doi: 10.48550/arxiv.1102.1144 · pith_short_12: 6MSS5EZIJ2JZ · pith_short_16: 6MSS5EZIJ2JZBWBQ · pith_short_8: 6MSS5EZI

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/6MSS5EZIJ2JZBWBQI3VLHPH2FO \
  | 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: f3252e93284e9390d83046eab3bcfa2ba08a69727f37cf90f5de8af2e403df06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e6e7bf35947c1be600435958eae962e20ba126f7dd6e8950f5f829649e5b15b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-06T12:12:42Z",
    "title_canon_sha256": "96f495a5c968b9e962d46d0c0658d6bd7be249be3eb52750e773db13e96fc221"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1144",
    "kind": "arxiv",
    "version": 1
  }
}