Pith Number

pith:PMKFZMLF

pith:2006:PMKFZMLFQPY7SVS5M4CYJPUBTV

not attested not anchored not stored refs pending

Lyapunov Exponents and Spectral Analysis of Ergodic Schr\"odinger Operators: A Survey of Kotani Theory and its Applications

David Damanik (Caltech)

arxiv:math-ph/0605054 v1 · 2006-05-17 · math-ph · math.DS · 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{PMKFZMLFQPY7SVS5M4CYJPUBTV}

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	2026-05-18T02:30:16.520336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b145cb16583f1f9565d670584be819d69dc136cef0cc74643c7b256e19bc4f3

Aliases

arxiv: math-ph/0605054 · arxiv_version: math-ph/0605054v1 · doi: 10.48550/arxiv.math-ph/0605054 · pith_short_12: PMKFZMLFQPY7 · pith_short_16: PMKFZMLFQPY7SVS5 · pith_short_8: PMKFZMLF

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/PMKFZMLFQPY7SVS5M4CYJPUBTV \
  | 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: 7b145cb16583f1f9565d670584be819d69dc136cef0cc74643c7b256e19bc4f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebaae8b9412f85f3b8d085cd0092bb0e4d64e415c8772fc4ad0ccceb9912547c",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-05-17T20:15:19Z",
    "title_canon_sha256": "e83f2b99e5c9fbe3f6537aad8016bd3baadd73f8d1911dc2138d7426461a486d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0605054",
    "kind": "arxiv",
    "version": 1
  }
}