Pith Number

pith:IIED22EL

pith:2011:IIED22EL6TXFGXFS5TP7RXN7WN

not attested not anchored not stored refs pending

Periodic and limit-periodic discrete Schr\"odinger operators

Helge Krueger

arxiv:1108.1584 v1 · 2011-08-07 · 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{IIED22EL6TXFGXFS5TP7RXN7WN}

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	2026-05-18T04:16:00.700510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42083d688bf4ee535cb2ecdff8ddbfb3621732a68e5c6c1f21200510b51363ec

Aliases

arxiv: 1108.1584 · arxiv_version: 1108.1584v1 · doi: 10.48550/arxiv.1108.1584 · pith_short_12: IIED22EL6TXF · pith_short_16: IIED22EL6TXFGXFS · pith_short_8: IIED22EL

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/IIED22EL6TXFGXFS5TP7RXN7WN \
  | 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: 42083d688bf4ee535cb2ecdff8ddbfb3621732a68e5c6c1f21200510b51363ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac1ce510ecb12151a5cab7972a5570cc0e5af5b94a8354487e7a71611d7f07a0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-08-07T22:49:24Z",
    "title_canon_sha256": "897a9ba36003d9d81cc5fe948998ab7400ca484d69dcd07889353b74b6929c87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1584",
    "kind": "arxiv",
    "version": 1
  }
}