Pith Number

pith:KG22GT2U

pith:2018:KG22GT2URVLAPFIMQC6WQXCL2T

not attested not anchored not stored refs pending

Equivalence between spectral properties of graphs with and without loops

Armando Bazzani, Daniel Remondini, Eleonora Andreotti

arxiv:1804.05988 v2 · 2018-04-17 · 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{KG22GT2URVLAPFIMQC6WQXCL2T}

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	2026-05-17T23:56:53.460471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51b5a34f548d5607950c80bd685c4bd4c331ad745706a3cd3ea8fb6926b5ac2e

Aliases

arxiv: 1804.05988 · arxiv_version: 1804.05988v2 · doi: 10.48550/arxiv.1804.05988 · pith_short_12: KG22GT2URVLA · pith_short_16: KG22GT2URVLAPFIM · pith_short_8: KG22GT2U

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/KG22GT2URVLAPFIMQC6WQXCL2T \
  | 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: 51b5a34f548d5607950c80bd685c4bd4c331ad745706a3cd3ea8fb6926b5ac2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d06e7ea32e351c00bdc78a2a46091d553e48e3d626e23da97991f89c0c89e21f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-04-17T00:08:17Z",
    "title_canon_sha256": "4d282cbbb7c740b1397d3f240a30508c69019088d00d5b3d42a43a48ee22e227"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.05988",
    "kind": "arxiv",
    "version": 2
  }
}