Pith Number

pith:U2TCMGWL

pith:2018:U2TCMGWLZ2YYV6GEGULY6APM2Z

not attested not anchored not stored refs pending

Counting eigenvalues of Schr\"odinger operator with complex fast decreasing potential

Alexander Borichev, Alexander Volberg, Rupert Frank

arxiv:1811.05591 v4 · 2018-11-14 · math.CA · math.CV · 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{U2TCMGWLZ2YYV6GEGULY6APM2Z}

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	2026-05-17T23:54:39.043841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6a6261acbceb18af8c435178f01ecd65fc661906461f56a9216155558c66de0

Aliases

arxiv: 1811.05591 · arxiv_version: 1811.05591v4 · doi: 10.48550/arxiv.1811.05591 · pith_short_12: U2TCMGWLZ2YY · pith_short_16: U2TCMGWLZ2YYV6GE · pith_short_8: U2TCMGWL

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/U2TCMGWLZ2YYV6GEGULY6APM2Z \
  | 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: a6a6261acbceb18af8c435178f01ecd65fc661906461f56a9216155558c66de0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3ca1a2bafaf4633fc8c321dd59cad831665bf72581addfe7df92b9b0e939209",
    "cross_cats_sorted": [
      "math.CV",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-11-14T01:30:56Z",
    "title_canon_sha256": "57e81f498773a4665f3f6b6ceaa59d840bf565fe297f4c2b6e15e999288a7e56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.05591",
    "kind": "arxiv",
    "version": 4
  }
}