Pith Number

pith:6Y3PS5WH

pith:2013:6Y3PS5WHXNRI3EUWZKAX5PVJEY

not attested not anchored not stored refs pending

Existence of the Stark-Wannier quantum resonances

Andrea Sacchetti

arxiv:1312.6066 v1 · 2013-12-20 · 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{6Y3PS5WHXNRI3EUWZKAX5PVJEY}

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	2026-05-18T01:45:43.192947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f636f976c7bb628d9296ca817ebea92604beca718b94634f8bb41a2013c95d76

Aliases

arxiv: 1312.6066 · arxiv_version: 1312.6066v1 · doi: 10.48550/arxiv.1312.6066 · pith_short_12: 6Y3PS5WHXNRI · pith_short_16: 6Y3PS5WHXNRI3EUW · pith_short_8: 6Y3PS5WH

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/6Y3PS5WHXNRI3EUWZKAX5PVJEY \
  | 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: f636f976c7bb628d9296ca817ebea92604beca718b94634f8bb41a2013c95d76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7c96f85687496ea8910d36540da82ec61972bdaac7cb93af9e14c11d9146018",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-12-20T18:30:15Z",
    "title_canon_sha256": "9142dafabb29bd5861370624620c9711f3ea830cd778c46b875fd66c4b73bc3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6066",
    "kind": "arxiv",
    "version": 1
  }
}