Pith Number

pith:CTY45M2W

pith:2010:CTY45M2WGCOODVEV5BBZPGGZOS

not attested not anchored not stored refs pending

Spectral properties of a limit-periodic Schr\"odinger operator in dimension two

Young-Ran Lee, Yulia Karpeshina

arxiv:1008.4632 v1 · 2010-08-27 · 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{CTY45M2WGCOODVEV5BBZPGGZOS}

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	2026-05-18T04:41:44.578311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14f1ceb356309ce1d495e8439798d974938a5572deb239abf17443f47ac38c98

Aliases

arxiv: 1008.4632 · arxiv_version: 1008.4632v1 · doi: 10.48550/arxiv.1008.4632 · pith_short_12: CTY45M2WGCOO · pith_short_16: CTY45M2WGCOODVEV · pith_short_8: CTY45M2W

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/CTY45M2WGCOODVEV5BBZPGGZOS \
  | 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: 14f1ceb356309ce1d495e8439798d974938a5572deb239abf17443f47ac38c98

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ec9ce133cd02c760f3db87494c0fc6cb252b9cd0b26a5a9334bd6f21258efac",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-08-27T02:15:25Z",
    "title_canon_sha256": "82e5836e8f19415fd230e00895962fa261ac97ac08bb929ad8d5c54d670a0a02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4632",
    "kind": "arxiv",
    "version": 1
  }
}