Pith Number

pith:77NK6GMZ

pith:2005:77NK6GMZ5FIASBGOOGF4NVRTQO

not attested not anchored not stored refs pending

Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schr\"{o}dinger operators

Alexander Fedotov (Department of Mathematical Physics), Fr\'ed\'eric Klopp (LAGA)

arxiv:math-ph/0502039 v1 · 2005-02-13 · 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{77NK6GMZ5FIASBGOOGF4NVRTQO}

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	2026-05-18T01:08:53.259496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffdaaf1999e9500904ce718bc6d63383be644ae3679af89bcd9992643658295c

Aliases

arxiv: math-ph/0502039 · arxiv_version: math-ph/0502039v1 · doi: 10.48550/arxiv.math-ph/0502039 · pith_short_12: 77NK6GMZ5FIA · pith_short_16: 77NK6GMZ5FIASBGO · pith_short_8: 77NK6GMZ

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/77NK6GMZ5FIASBGOOGF4NVRTQO \
  | 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: ffdaaf1999e9500904ce718bc6d63383be644ae3679af89bcd9992643658295c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d715aa6586018800bb03c64755b18eab6a6ba896342b71793e81c3ab0c90f29",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-02-13T18:21:11Z",
    "title_canon_sha256": "6ccc76ccda8ad84255fa6de094bdcfa01fa2360ad02bee8dec61d885b13c3836"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0502039",
    "kind": "arxiv",
    "version": 1
  }
}