Pith Number

pith:T6SKKAPG

pith:2017:T6SKKAPGLRY7WRTHWK5K5WQ3A6

not attested not anchored not stored refs pending

Asymptotics of spectral gaps of quasi-periodic Schr\"odinger operators

Jiangong You, Martin Leguil, Qi Zhou, Zhiyan Zhao

arxiv:1712.04700 v1 · 2017-12-13 · math.DS · 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{T6SKKAPGLRY7WRTHWK5K5WQ3A6}

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	2026-05-18T00:28:03.667788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fa4a501e65c71fb4667b2baaeda1b07a74b6f773d9655c9af626b82856155cb

Aliases

arxiv: 1712.04700 · arxiv_version: 1712.04700v1 · doi: 10.48550/arxiv.1712.04700 · pith_short_12: T6SKKAPGLRY7 · pith_short_16: T6SKKAPGLRY7WRTH · pith_short_8: T6SKKAPG

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/T6SKKAPGLRY7WRTHWK5K5WQ3A6 \
  | 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: 9fa4a501e65c71fb4667b2baaeda1b07a74b6f773d9655c9af626b82856155cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2acf878ca2ee41a38863c2a69f0e5bafaf6b34452cb54ef8e91c029d6faf75f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-12-13T10:57:13Z",
    "title_canon_sha256": "36c23f510b4da074c8947fc288a25902830a6fc1ebf4b33e1278f7f57a6e960e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.04700",
    "kind": "arxiv",
    "version": 1
  }
}