Pith Number

pith:H4ETUX2E

pith:2018:H4ETUX2ECYWG3BKNMZV42B2GVI

not attested not anchored not stored refs pending

New lower bounds for the Estrada and Signless Laplacian Estrada Index of a Graph

Jonnathan Rodr\'iguez, Juan L. Aguayo, Juan R. Carmona

arxiv:1810.04120 v3 · 2018-10-09 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H4ETUX2ECYWG3BKNMZV42B2GVI}

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	2026-05-17T23:42:02.960873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f093a5f44162c6d854d666bcd0746aa34086090a067ee5ce650d182e581c639

Aliases

arxiv: 1810.04120 · arxiv_version: 1810.04120v3 · doi: 10.48550/arxiv.1810.04120 · pith_short_12: H4ETUX2ECYWG · pith_short_16: H4ETUX2ECYWG3BKN · pith_short_8: H4ETUX2E

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/H4ETUX2ECYWG3BKNMZV42B2GVI \
  | 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: 3f093a5f44162c6d854d666bcd0746aa34086090a067ee5ce650d182e581c639

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb3088d575c7db76716fb7ce0d34d5e2a93d282d123e202c5cf3cb7799f7d0a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-10-09T16:49:15Z",
    "title_canon_sha256": "28dc1c3156395ba8b2bd9eebce1c6ba31ccb3958d0d819a8df3e60989aec7aee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.04120",
    "kind": "arxiv",
    "version": 3
  }
}