Pith Number

pith:7M7VVH7H

pith:2023:7M7VVH7HEOCOAWKWI4EOWD3UCF

not attested not anchored not stored refs pending

Sharp semiclassical spectral asymptotics for Schr\"odinger operators with non-smooth potentials

S{\o}ren Mikkelsen

arxiv:2309.12015 v2 · 2023-09-21 · math.SP · 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{7M7VVH7HEOCOAWKWI4EOWD3UCF}

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.

Cited by

1 paper in Pith

Commutator Estimates and Quantitative Local Weyl's Law for Schr\"odinger Operators with Non-Smooth Potentials

Receipt and verification

First computed	2026-07-05T09:04:29.474606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb3f5a9fe72384e059564708eb0f74117ecf54bfdc813e48ce297fdf75e6ad26

Aliases

arxiv: 2309.12015 · arxiv_version: 2309.12015v2 · doi: 10.48550/arxiv.2309.12015 · pith_short_12: 7M7VVH7HEOCO · pith_short_16: 7M7VVH7HEOCOAWKW · pith_short_8: 7M7VVH7H

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/7M7VVH7HEOCOAWKWI4EOWD3UCF \
  | 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: fb3f5a9fe72384e059564708eb0f74117ecf54bfdc813e48ce297fdf75e6ad26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "722c900bbfd8fbd531d3af8cd59483a288a9f3e15234105abb2b7fc6ee1f281b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2023-09-21T12:34:40Z",
    "title_canon_sha256": "5cb77b0bc08254b639dfb93a725bede53f82deaaa5a4e6299e0f63ff57bf7a3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2309.12015",
    "kind": "arxiv",
    "version": 2
  }
}