Pith Number

pith:FEXPBJZJ

pith:2015:FEXPBJZJHAVLHD7MHF4QQHNYIH

not attested not anchored not stored refs pending

Novel Bounds for the Normalized Laplacian Estrada and Normalized Energy Index of Graphs

Alessandra Cornaro, Gian Paolo Clemente

arxiv:1508.00385 v2 · 2015-08-03 · 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{FEXPBJZJHAVLHD7MHF4QQHNYIH}

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	2026-05-18T00:52:04.256323Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

292ef0a729382ab38fec3979081db841d4c14853c4de1c2581ede82a10138b74

Aliases

arxiv: 1508.00385 · arxiv_version: 1508.00385v2 · doi: 10.48550/arxiv.1508.00385 · pith_short_12: FEXPBJZJHAVL · pith_short_16: FEXPBJZJHAVLHD7M · pith_short_8: FEXPBJZJ

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/FEXPBJZJHAVLHD7MHF4QQHNYIH \
  | 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: 292ef0a729382ab38fec3979081db841d4c14853c4de1c2581ede82a10138b74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2578f73582f38a7d8e3667344d2950f0a537d7b4393323bbf4acd8ae97e53bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-03T11:59:56Z",
    "title_canon_sha256": "34a97e3a001d0a75ef3fe89d0086a137c644f11a6948024923859d990059ce29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.00385",
    "kind": "arxiv",
    "version": 2
  }
}