Pith Number

pith:PO7TL7EQ

pith:2011:PO7TL7EQJ5MXFM5YP23FTO3Y4N

not attested not anchored not stored refs pending

A Schauder and Riesz Basis Criterion for Non-Self-Adjoint Schr\"odinger Operators with Periodic and Antiperiodic Boundary Conditions

Fritz Gesztesy, Vadim Tkachenko

arxiv:1104.4846 v2 · 2011-04-26 · math.SP · math.CA · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PO7TL7EQJ5MXFM5YP23FTO3Y4N}

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	2026-05-18T04:20:39.334531Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bbf35fc904f5972b3b87eb659bb78e34952c2c98007a78bb06dd65862ec7118

Aliases

arxiv: 1104.4846 · arxiv_version: 1104.4846v2 · doi: 10.48550/arxiv.1104.4846 · pith_short_12: PO7TL7EQJ5MX · pith_short_16: PO7TL7EQJ5MXFM5Y · pith_short_8: PO7TL7EQ

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/PO7TL7EQJ5MXFM5YP23FTO3Y4N \
  | 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: 7bbf35fc904f5972b3b87eb659bb78e34952c2c98007a78bb06dd65862ec7118

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31de2b990100782afe7a155f750bd48945ce5367d17a66563e5463ed0a817f36",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-04-26T06:34:14Z",
    "title_canon_sha256": "d044382e3b94df1d97a9108f1b8a2fe669573a188d3261bfee9e9ee2a54d44e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.4846",
    "kind": "arxiv",
    "version": 2
  }
}