Pith Number

pith:A5WZNG3Y

pith:1999:A5WZNG3Y75R3C65E7S2P4AHQLI

not attested not anchored not stored refs pending

On absence of embedded eigenvalues for Schr\"{o}dinger operators with perturbed periodic potentials

Boris Vainberg, Peter Kuchment

arxiv:math-ph/9904016 v1 · 1999-04-16 · math-ph · math.MP · 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{A5WZNG3Y75R3C65E7S2P4AHQLI}

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	2026-07-04T14:34:10.216068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

076d969b78ff63b17ba4fcb4fe00f05a0b5d5fc44564273989e7eac48cc1e0d0

Aliases

arxiv: math-ph/9904016 · arxiv_version: math-ph/9904016v1 · doi: 10.48550/arxiv.math-ph/9904016 · pith_short_12: A5WZNG3Y75R3 · pith_short_16: A5WZNG3Y75R3C65E · pith_short_8: A5WZNG3Y

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/A5WZNG3Y75R3C65E7S2P4AHQLI \
  | 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: 076d969b78ff63b17ba4fcb4fe00f05a0b5d5fc44564273989e7eac48cc1e0d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7f382544a83a7062fe5f06db91135424596be73a6457c20568d716e626ea87f",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "1999-04-16T22:08:08Z",
    "title_canon_sha256": "83394d1d8e6246ada848eac6a8f47330d164f8c344483bc7dc2a470b3b9b64ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/9904016",
    "kind": "arxiv",
    "version": 1
  }
}