Pith Number

pith:RHU4X6IY

pith:2021:RHU4X6IYG4UQETBVFPOQ5PEMPY

not attested not anchored not stored refs pending

Laplace and Schr\"odinger operators without eigenvalues on homogeneous amenable graphs

Christophe Pittet, Rostislav Grigorchuk

arxiv:2102.13542 v4 · 2021-02-26 · math.SP · math-ph · math.GR · 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{RHU4X6IYG4UQETBVFPOQ5PEMPY}

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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.

Cited by

1 paper in Pith

Random Schr\"odinger operators and convolution on wreath products

Receipt and verification

First computed	2026-07-05T05:28:41.447904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89e9cbf9183729024c352bdd0ebc8c7e0d3c83f95a5f118b2ece53fb5e2855c7

Aliases

arxiv: 2102.13542 · arxiv_version: 2102.13542v4 · doi: 10.48550/arxiv.2102.13542 · pith_short_12: RHU4X6IYG4UQ · pith_short_16: RHU4X6IYG4UQETBV · pith_short_8: RHU4X6IY

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/RHU4X6IYG4UQETBVFPOQ5PEMPY \
  | 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: 89e9cbf9183729024c352bdd0ebc8c7e0d3c83f95a5f118b2ece53fb5e2855c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca8e51624f9d398ae12bf748c21907e1254d18ee1301e6cf5253ca5b91aeb38c",
    "cross_cats_sorted": [
      "math-ph",
      "math.GR",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2021-02-26T15:30:59Z",
    "title_canon_sha256": "8fbcf44e281874baaacaa04291ffdcc91d164ebcf831a1067ee988c73308d16d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.13542",
    "kind": "arxiv",
    "version": 4
  }
}