Pith Number

pith:ZXGQXJ3Z

pith:2012:ZXGQXJ3ZADKXGSMIUWGJGB3VEW

not attested not anchored not stored refs pending

A class of Schrodinger operators with decaying oscillatory potentials

Milivoje Lukic

arxiv:1207.5077 v1 · 2012-07-20 · 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{ZXGQXJ3ZADKXGSMIUWGJGB3VEW}

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	2026-05-18T01:56:15.486245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdcd0ba77900d5734988a58c93077525902498f328616be69e3858f1ff7ee2f5

Aliases

arxiv: 1207.5077 · arxiv_version: 1207.5077v1 · doi: 10.48550/arxiv.1207.5077 · pith_short_12: ZXGQXJ3ZADKX · pith_short_16: ZXGQXJ3ZADKXGSMI · pith_short_8: ZXGQXJ3Z

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/ZXGQXJ3ZADKXGSMIUWGJGB3VEW \
  | 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: cdcd0ba77900d5734988a58c93077525902498f328616be69e3858f1ff7ee2f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93acda5aedbfc9c936268fa340c3accb54194c7253d149cc91cd082fdd1d2afe",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-07-20T23:36:13Z",
    "title_canon_sha256": "e0b223315fbcce43b8241f8457c53f8b11d60dde85dcc643333bea8d136c958d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5077",
    "kind": "arxiv",
    "version": 1
  }
}