Pith Number

pith:YV6LDYTK

pith:2026:YV6LDYTKD7SGVZUAANHJ4JMTHB

not attested not anchored not stored refs pending

Cantor Spectrum via a Reducibility-Duality Bridge for the Mosaic Almost Mathieu Operator

Jiawei He, Yongjian Wang, Yuan Shan

arxiv:2606.23422 v1 · 2026-06-22 · 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{YV6LDYTKD7SGVZUAANHJ4JMTHB}

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	2026-06-23T03:14:19.603449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c57cb1e26a1fe46ae680034e9e25933859a39096170fa443098b41b39047e2a6

Aliases

arxiv: 2606.23422 · arxiv_version: 2606.23422v1 · doi: 10.48550/arxiv.2606.23422 · pith_short_12: YV6LDYTKD7SG · pith_short_16: YV6LDYTKD7SGVZUA · pith_short_8: YV6LDYTK

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/YV6LDYTKD7SGVZUAANHJ4JMTHB \
  | 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: c57cb1e26a1fe46ae680034e9e25933859a39096170fa443098b41b39047e2a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8cfcbaff2772d1ebcd751da23a5dd03aef269b6e637e0d0007bf7b62eab2f359",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-22T14:45:24Z",
    "title_canon_sha256": "441adaaa9843674cfa55eff43b0eb902dc685c31e3eb6c757a7cabfd4657ec57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23422",
    "kind": "arxiv",
    "version": 1
  }
}