Pith Number

pith:D7X4INUF

pith:2006:D7X4INUF6AZ7IQJ6PLZV4CXV53

not attested not anchored not stored refs pending

The width of resonances for slowly varying perturbations of one-dimensional periodic Schr\"{o}dinger operators

Fr\'ed\'eric Klopp (LAGA), Magali Marx (IF)

arxiv:math-ph/0605031 v1 · 2006-05-09 · 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{D7X4INUF6AZ7IQJ6PLZV4CXV53}

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	2026-05-18T01:08:51.682642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fefc43685f033f4413e7af35e0af5eeeec3910fd7f27917c00e5e20a1a760e9

Aliases

arxiv: math-ph/0605031 · arxiv_version: math-ph/0605031v1 · doi: 10.48550/arxiv.math-ph/0605031 · pith_short_12: D7X4INUF6AZ7 · pith_short_16: D7X4INUF6AZ7IQJ6 · pith_short_8: D7X4INUF

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/D7X4INUF6AZ7IQJ6PLZV4CXV53 \
  | 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: 1fefc43685f033f4413e7af35e0af5eeeec3910fd7f27917c00e5e20a1a760e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e642a89ed95bc14e810e81e88228fd62bab5ced7c6c223eca77191c9ade616cb",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-05-09T12:04:48Z",
    "title_canon_sha256": "0faeff0ee6091de2783c2de5aedba4f4ece90f779aad74ab8968e3de7e6b2d9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0605031",
    "kind": "arxiv",
    "version": 1
  }
}