Pith Number

pith:VKUJANMB

pith:2025:VKUJANMB7MVTUYHNT2L2JE3RA7

not attested not anchored not stored refs pending

Cantor spectrum for multidimensional quasi-periodic Schr\"odinger operators

Bernard Helffer, Qinghui Liu, Qi Zhou, Yanhui Qu

arxiv:2506.03577 v1 · 2025-06-04 · math.SP · math-ph · math.DS · math.MG · 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{VKUJANMB7MVTUYHNT2L2JE3RA7}

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	2026-06-19T16:10:29.920139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaa8903581fb2b3a60ed9e97a4937107cf8df0652b31a643a53942309af2faa4

Aliases

arxiv: 2506.03577 · arxiv_version: 2506.03577v1 · doi: 10.48550/arxiv.2506.03577 · pith_short_12: VKUJANMB7MVT · pith_short_16: VKUJANMB7MVTUYHN · pith_short_8: VKUJANMB

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/VKUJANMB7MVTUYHNT2L2JE3RA7 \
  | 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: aaa8903581fb2b3a60ed9e97a4937107cf8df0652b31a643a53942309af2faa4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcbe90f44e0571e991c81d0fef146eb1e666a4316dec08a0112c8f8c1f654712",
    "cross_cats_sorted": [
      "math-ph",
      "math.DS",
      "math.MG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2025-06-04T04:53:00Z",
    "title_canon_sha256": "32951b1150a7555200c836d466827ae2cee05f8c32ef6b8168e940b37e9e8638"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.03577",
    "kind": "arxiv",
    "version": 1
  }
}