Pith Number

pith:NLUP7WNI

pith:2016:NLUP7WNIEW4ZSM3P5F26SRRTY2

not attested not anchored not stored refs pending

Quantitative bounds versus existence of weakly coupled bound states for Schr\"odinger type operators

Dirk Hundertmark, Johanna Richter, Semjon Vugalter, Vu Hoang

arxiv:1610.09891 v2 · 2016-10-31 · 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{NLUP7WNIEW4ZSM3P5F26SRRTY2}

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	2026-05-18T00:44:09.298431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ae8ffd9a825b999336fe975e94633c69d6d9d69b9615485503213b2edad32ea

Aliases

arxiv: 1610.09891 · arxiv_version: 1610.09891v2 · doi: 10.48550/arxiv.1610.09891 · pith_short_12: NLUP7WNIEW4Z · pith_short_16: NLUP7WNIEW4ZSM3P · pith_short_8: NLUP7WNI

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/NLUP7WNIEW4ZSM3P5F26SRRTY2 \
  | 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: 6ae8ffd9a825b999336fe975e94633c69d6d9d69b9615485503213b2edad32ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b58124f07c9e5d27288a566e766e32885a967c555a9c568e01fa355656da7b4",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-10-31T12:18:29Z",
    "title_canon_sha256": "7797be8401e7563dce625c2348f2636c614b91951ba6ce105894f838226fdf31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.09891",
    "kind": "arxiv",
    "version": 2
  }
}