Pith Number

pith:4QUXFRTM

pith:2014:4QUXFRTM4DFKX65YSMDQOB5ULK

not attested not anchored not stored refs pending

Isospectrality for graph Laplacians under the change of coupling at graph vertices: necessary and sufficient conditions

Alexander V. Kiselev, Irina I. Karpenko, Yulia Ershova

arxiv:1405.5016 v2 · 2014-05-20 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4QUXFRTM4DFKX65YSMDQOB5ULK}

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	2026-05-18T01:25:03.642367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e42972c66ce0caabfbb893070707b45ab0212e60b21d72e3b9d3c842f7e56986

Aliases

arxiv: 1405.5016 · arxiv_version: 1405.5016v2 · doi: 10.48550/arxiv.1405.5016 · pith_short_12: 4QUXFRTM4DFK · pith_short_16: 4QUXFRTM4DFKX65Y · pith_short_8: 4QUXFRTM

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/4QUXFRTM4DFKX65YSMDQOB5ULK \
  | 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: e42972c66ce0caabfbb893070707b45ab0212e60b21d72e3b9d3c842f7e56986

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a92a1d682424cf35a9746d4e4b9544ebec53682ab9f703860b8e87ff5135641",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2014-05-20T10:00:09Z",
    "title_canon_sha256": "bfad37958341e873bd19df39654edb5ba6abd808066d8dc85dda636d53b6b2eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.5016",
    "kind": "arxiv",
    "version": 2
  }
}