Pith Number

pith:XSG3UWWP

pith:2011:XSG3UWWPJHRW7DI55XDYN5N6OB

not attested not anchored not stored refs pending

Semiclassical spectral asymptotics for a two-dimensional magnetic Schr\"odinger operator II: The case of degenerate wells

Bernard Helffer, Yuri A. Kordyukov

arxiv:1103.4326 v1 · 2011-03-22 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XSG3UWWPJHRW7DI55XDYN5N6OB}

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	2026-05-18T04:26:12.559740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc8dba5acf49e36f8d1dedc786f5be706bbcfb2f3d920b8bb299aedb3c2713e6

Aliases

arxiv: 1103.4326 · arxiv_version: 1103.4326v1 · doi: 10.48550/arxiv.1103.4326 · pith_short_12: XSG3UWWPJHRW · pith_short_16: XSG3UWWPJHRW7DI5 · pith_short_8: XSG3UWWP

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/XSG3UWWPJHRW7DI55XDYN5N6OB \
  | 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: bc8dba5acf49e36f8d1dedc786f5be706bbcfb2f3d920b8bb299aedb3c2713e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04af51fb6825cb0e9912fb2e44c0dfb2b90e1497d94edab1609ec30b67a79db4",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-03-22T17:47:19Z",
    "title_canon_sha256": "b51d94a890c1bfd9936720b68f4e6cd981b52ef1e5d90452b6ec0974c9a03211"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4326",
    "kind": "arxiv",
    "version": 1
  }
}