Pith Number

pith:2RCKAF7Z

pith:2020:2RCKAF7ZRHZWG7GCV7CO4YG3HL

not attested not anchored not stored refs pending

Eigenvalues of the normalized complex Laplacian on finite electrical networks

Anna Muranova, Robert Schippa

arxiv:2012.12759 v1 · 2020-12-23 · math.SP · 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{2RCKAF7ZRHZWG7GCV7CO4YG3HL}

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	2026-06-19T16:11:07.038605Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d444a017f989f3637cc2afc4ee60db3af581376bb0bdb12741a5ed5169cdf430

Aliases

arxiv: 2012.12759 · arxiv_version: 2012.12759v1 · doi: 10.48550/arxiv.2012.12759 · pith_short_12: 2RCKAF7ZRHZW · pith_short_16: 2RCKAF7ZRHZWG7GC · pith_short_8: 2RCKAF7Z

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/2RCKAF7ZRHZWG7GCV7CO4YG3HL \
  | 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: d444a017f989f3637cc2afc4ee60db3af581376bb0bdb12741a5ed5169cdf430

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72768d4ad639e2a647bb85cd60a34ca179e98371df0d9ac5c883a51a6d9c8e81",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2020-12-23T15:56:40Z",
    "title_canon_sha256": "0bdd956e79a1c2f73bafcf103f1e377d3cebdc938058eec5f31522a1f94f9597"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.12759",
    "kind": "arxiv",
    "version": 1
  }
}