Pith Number

pith:R5EJD75J

pith:2012:R5EJD75JZPACYNLCRJ7W5L7KIG

not attested not anchored not stored refs pending

On the $l^p$ spectrum of Laplacians on graphs

Bobo Hua, Frank Bauer, Matthias Keller

arxiv:1211.6536 v1 · 2012-11-28 · math.SP · math-ph · math.FA · 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{R5EJD75JZPACYNLCRJ7W5L7KIG}

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	2026-05-18T03:39:51.274475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f4891ffa9cbc02c35628a7f6eafea4199810d871358737ed9d707253036f4db

Aliases

arxiv: 1211.6536 · arxiv_version: 1211.6536v1 · doi: 10.48550/arxiv.1211.6536 · pith_short_12: R5EJD75JZPAC · pith_short_16: R5EJD75JZPACYNLC · pith_short_8: R5EJD75J

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/R5EJD75JZPACYNLCRJ7W5L7KIG \
  | 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: 8f4891ffa9cbc02c35628a7f6eafea4199810d871358737ed9d707253036f4db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e6ba8107873b9f3cdc7c9d0b9d75a52e4a67b2eb1e7ada5f368f47f48bb8346",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-11-28T08:12:44Z",
    "title_canon_sha256": "f581f65f2aef2b1077c8ead7437795e047c220d86e982db78f7089e193e54b12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6536",
    "kind": "arxiv",
    "version": 1
  }
}