Pith Number

pith:KEQMZBBN

pith:2018:KEQMZBBNU3IYNDW7HAOT4ZRDWE

not attested not anchored not stored refs pending

Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic Jacobi operators

Darren C. Ong, Wencai Liu

arxiv:1805.01571 v2 · 2018-05-03 · math.SP · 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{KEQMZBBNU3IYNDW7HAOT4ZRDWE}

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	2026-05-18T00:04:07.712250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5120cc842da6d1868edf381d3e6623b11344650c2ab8ff873d181bca19cc96c3

Aliases

arxiv: 1805.01571 · arxiv_version: 1805.01571v2 · doi: 10.48550/arxiv.1805.01571 · pith_short_12: KEQMZBBNU3IY · pith_short_16: KEQMZBBNU3IYNDW7 · pith_short_8: KEQMZBBN

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/KEQMZBBNU3IYNDW7HAOT4ZRDWE \
  | 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: 5120cc842da6d1868edf381d3e6623b11344650c2ab8ff873d181bca19cc96c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2de87d33d1b00c331b289d10aee33de3c32bb27440c497a1ad97a0340683bbb",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-05-03T23:13:21Z",
    "title_canon_sha256": "af088c697d5433753030a2f1f98ab135633607ee7f3bd7c639f9421f7a335cf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.01571",
    "kind": "arxiv",
    "version": 2
  }
}