Pith Number

pith:J66YZTYJ

pith:2009:J66YZTYJEPSNPZF3OYWHU2ATRT

not attested not anchored not stored refs pending

Limit-Periodic Schr\"odinger Operators in the Regime of Positive Lyapunov Exponents

David Damanik, Zheng Gan

arxiv:0906.3340 v3 · 2009-06-18 · math.SP · math-ph · math.FA · 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{J66YZTYJEPSNPZF3OYWHU2ATRT}

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	2026-05-18T02:30:16.156157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4fbd8ccf0923e4d7e4bb762c7a68138cd9786ad6cd8804cfdc05493d4b4be7a5

Aliases

arxiv: 0906.3340 · arxiv_version: 0906.3340v3 · doi: 10.48550/arxiv.0906.3340 · pith_short_12: J66YZTYJEPSN · pith_short_16: J66YZTYJEPSNPZF3 · pith_short_8: J66YZTYJ

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/J66YZTYJEPSNPZF3OYWHU2ATRT \
  | 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: 4fbd8ccf0923e4d7e4bb762c7a68138cd9786ad6cd8804cfdc05493d4b4be7a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab03d6602f46b166690e167635dcd83c92f7f4a0addd53fbcb0999c81d2f232b",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2009-06-18T02:33:30Z",
    "title_canon_sha256": "9d855779c008a21d3394145e839c403f90458c300cd2193d72b9f35f6150b39a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.3340",
    "kind": "arxiv",
    "version": 3
  }
}