Pith Number

pith:GW7TN2QY

pith:2019:GW7TN2QYAMCKU7XGDMD3NKYSTB

not attested not anchored not stored refs pending

Conditions for discreteness of the spectrum to multi-dimensional Schr\"odinger operator

Leonid Zelenko

arxiv:1906.02186 v1 · 2019-06-05 · 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{GW7TN2QYAMCKU7XGDMD3NKYSTB}

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	2026-05-17T23:44:01.934599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35bf36ea180304aa7ee61b07b6ab129852be59a0f75f09beeae3a6e23a418b43

Aliases

arxiv: 1906.02186 · arxiv_version: 1906.02186v1 · doi: 10.48550/arxiv.1906.02186 · pith_short_12: GW7TN2QYAMCK · pith_short_16: GW7TN2QYAMCKU7XG · pith_short_8: GW7TN2QY

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/GW7TN2QYAMCKU7XGDMD3NKYSTB \
  | 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: 35bf36ea180304aa7ee61b07b6ab129852be59a0f75f09beeae3a6e23a418b43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2063a5d458961b91104ae9d11f09c5e59b1649415aa6ff205fd86ba3a294cb0a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2019-06-05T11:06:43Z",
    "title_canon_sha256": "a749fc5883105744d73b7418abb68d879e620f0ffd89ed97931bbba31bf8ba7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.02186",
    "kind": "arxiv",
    "version": 1
  }
}