Pith Number

pith:URTRKTE7

pith:2018:URTRKTE7ZTTXIVLHN2AHMGFC36

not attested not anchored not stored refs pending

A Borg-Levinson theorem for magnetic Schr\"odinger operators on a Riemannian manifold

Dos Santos Ferreira, Mourad Bellassoued, Mourad Choulli, Plamen Stefanov, Yavar Kian

arxiv:1807.08857 v2 · 2018-07-23 · math.AP · math-ph · 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{URTRKTE7ZTTXIVLHN2AHMGFC36}

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	2026-05-18T00:02:09.425099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a467154c9fcce77455676e807618a2dfb6009f65a56e34899087941effb54998

Aliases

arxiv: 1807.08857 · arxiv_version: 1807.08857v2 · doi: 10.48550/arxiv.1807.08857 · pith_short_12: URTRKTE7ZTTX · pith_short_16: URTRKTE7ZTTXIVLH · pith_short_8: URTRKTE7

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/URTRKTE7ZTTXIVLHN2AHMGFC36 \
  | 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: a467154c9fcce77455676e807618a2dfb6009f65a56e34899087941effb54998

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "486289848fd405c43764686a0816954011aa4fd098dacad3b7fadafc1a39b4ca",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-07-23T23:39:39Z",
    "title_canon_sha256": "f7adbcaf609a2efc346b32e9e223c4c075d78f1207894cf805306c36fb02264a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.08857",
    "kind": "arxiv",
    "version": 2
  }
}