Pith Number

pith:2HLLSVEP

pith:2026:2HLLSVEPBPPEC7VR4A7POSG7QX

not attested not anchored not stored refs pending

A doubled Gordon threshold for palindromic quasiperiodic Schr\"odinger operators

Wencai Liu

arxiv:2607.24188 v1 · 2026-07-27 · math-ph · math.MP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2HLLSVEPBPPEC7VR4A7POSG7QX}

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	2026-07-28T02:23:49.927289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1d6b9548f0bde417eb1e03ef748df85c5c3f2800f9f2786f21127a6ac7536d3

Aliases

arxiv: 2607.24188 · arxiv_version: 2607.24188v1 · doi: 10.48550/arxiv.2607.24188 · pith_short_12: 2HLLSVEPBPPE · pith_short_16: 2HLLSVEPBPPEC7VR · pith_short_8: 2HLLSVEP

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/2HLLSVEPBPPEC7VR4A7POSG7QX \
  | 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: d1d6b9548f0bde417eb1e03ef748df85c5c3f2800f9f2786f21127a6ac7536d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "301e0e5aade227805a1176a8ef3ccf4f60577d36c3a10c3e380b3d72bc7cb4dc",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-27T09:07:52Z",
    "title_canon_sha256": "621f4f43d8d1ec785266d4269490ccaed81a2d0554c39488afe44e091cbe79dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24188",
    "kind": "arxiv",
    "version": 1
  }
}