Pith Number

pith:UF4BNKR4

pith:2018:UF4BNKR4HQDOOVEMWMNGO3KDNJ

not attested not anchored not stored refs pending

Conditions of discreteness of the spectrum for Schr\"odinger operator and some optimization problems for capacity and measures

Leonid Zelenko

arxiv:1812.00416 v1 · 2018-12-02 · math.SP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UF4BNKR4HQDOOVEMWMNGO3KDNJ}

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	2026-05-17T23:59:21.409543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a17816aa3c3c06e7548cb31a676d436a705da24d2667ea2053bc4a7d4f449c90

Aliases

arxiv: 1812.00416 · arxiv_version: 1812.00416v1 · doi: 10.48550/arxiv.1812.00416 · pith_short_12: UF4BNKR4HQDO · pith_short_16: UF4BNKR4HQDOOVEM · pith_short_8: UF4BNKR4

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/UF4BNKR4HQDOOVEMWMNGO3KDNJ \
  | 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: a17816aa3c3c06e7548cb31a676d436a705da24d2667ea2053bc4a7d4f449c90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2897fd5345e2ca907918a85f5205cd61b27009f15bdc791b90b349982f3b7f30",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-12-02T16:15:17Z",
    "title_canon_sha256": "5bc1570d7ce7938398e2cbfadeb17e966db3529af11e6aa84d9f05da03429800"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.00416",
    "kind": "arxiv",
    "version": 1
  }
}