Pith Number

pith:LXQK2XAA

pith:2009:LXQK2XAAJEQPHCFBGDI3VLH4TD

not attested not anchored not stored refs pending

A Description of All Self-Adjoint Extensions of the Laplacian and Krein-Type Resolvent Formulas on Nonsmooth Domains

Fritz Gesztesy, Marius Mitrea

arxiv:0907.1750 v4 · 2009-07-10 · math.AP · 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{LXQK2XAAJEQPHCFBGDI3VLH4TD}

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	2026-05-18T02:44:08.807530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5de0ad5c004920f388a130d1baacfc98e40f5f9b8a2c1bbdb601d55a80a3b06c

Aliases

arxiv: 0907.1750 · arxiv_version: 0907.1750v4 · doi: 10.48550/arxiv.0907.1750 · pith_short_12: LXQK2XAAJEQP · pith_short_16: LXQK2XAAJEQPHCFB · pith_short_8: LXQK2XAA

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/LXQK2XAAJEQPHCFBGDI3VLH4TD \
  | 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: 5de0ad5c004920f388a130d1baacfc98e40f5f9b8a2c1bbdb601d55a80a3b06c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4eb449c4368d1306ff6e6ade315e1f729fa75398fdfd7b7374890f63252fb5e2",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-07-10T16:56:42Z",
    "title_canon_sha256": "aebee62a80541ea12207e70ca7d4d7956c43551c53b6ae4c0b4e669b30a5a5dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.1750",
    "kind": "arxiv",
    "version": 4
  }
}