Pith Number

pith:2EOI2RJY

pith:2011:2EOI2RJY4OODIXOMYLRWQTQ2FJ

not attested not anchored not stored refs pending

On the negative spectrum of two-dimensional Schr\"odinger operators with radial potentials

Ari Laptev, Michael Solomyak

arxiv:1108.1002 v3 · 2011-08-04 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2EOI2RJY4OODIXOMYLRWQTQ2FJ}

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	2026-05-18T00:37:37.966190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d11c8d4538e39c345dccc2e3684e1a2a6bd656bdf37c1fd0e078b7fb36fed4ec

Aliases

arxiv: 1108.1002 · arxiv_version: 1108.1002v3 · doi: 10.48550/arxiv.1108.1002 · pith_short_12: 2EOI2RJY4OOD · pith_short_16: 2EOI2RJY4OODIXOM · pith_short_8: 2EOI2RJY

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/2EOI2RJY4OODIXOMYLRWQTQ2FJ \
  | 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: d11c8d4538e39c345dccc2e3684e1a2a6bd656bdf37c1fd0e078b7fb36fed4ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4afdf0e4b33968f18827a313a0527ebb14d2ab94bafd75165682680666dcb24c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-08-04T06:39:39Z",
    "title_canon_sha256": "ce343a6ec1c466d1dc3a6b0ced602be3f1ebec98e5f4d82a396b41843e39ae51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1002",
    "kind": "arxiv",
    "version": 3
  }
}