Pith Number

pith:N6MBBJBN

pith:2015:N6MBBJBNA4X4MQU43JY7SVCWXS

not attested not anchored not stored refs pending

Virtual bound levels in a gap of the essential spectrum of the Schroedinger operator with a weakly perturbed periodic potential

Leonid Zelenko

arxiv:1505.07381 v1 · 2015-05-27 · 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{N6MBBJBNA4X4MQU43JY7SVCWXS}

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	2026-05-18T02:02:04.625574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f9810a42d072fc6429cda71f95456bc93b4dca1399ae53832fca766660272da

Aliases

arxiv: 1505.07381 · arxiv_version: 1505.07381v1 · doi: 10.48550/arxiv.1505.07381 · pith_short_12: N6MBBJBNA4X4 · pith_short_16: N6MBBJBNA4X4MQU4 · pith_short_8: N6MBBJBN

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/N6MBBJBNA4X4MQU43JY7SVCWXS \
  | 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: 6f9810a42d072fc6429cda71f95456bc93b4dca1399ae53832fca766660272da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0558faa10e17cc713a7b634996d179f7f107bfc92405a3a94870e856d2c69d28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-05-27T15:39:35Z",
    "title_canon_sha256": "d65d8d1a5410cb5c1aed9dfacf0fd157b2b6c0133eb09373dbf79c32de9941a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.07381",
    "kind": "arxiv",
    "version": 1
  }
}