Pith Number

pith:47QJIHKO

pith:2016:47QJIHKOVIXCWBNCEPVXLVJVPJ

not attested not anchored not stored refs pending

Central spectral gaps of the almost Mathieu operator

I. Krasovsky

arxiv:1602.08624 v2 · 2016-02-27 · 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{47QJIHKOVIXCWBNCEPVXLVJVPJ}

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	2026-05-18T00:57:31.331364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7e0941d4eaa2e2b05a223eb75d5357a6db9f7e4cf915e8ea61037eb9a7523e4

Aliases

arxiv: 1602.08624 · arxiv_version: 1602.08624v2 · doi: 10.48550/arxiv.1602.08624 · pith_short_12: 47QJIHKOVIXC · pith_short_16: 47QJIHKOVIXCWBNC · pith_short_8: 47QJIHKO

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/47QJIHKOVIXCWBNCEPVXLVJVPJ \
  | 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: e7e0941d4eaa2e2b05a223eb75d5357a6db9f7e4cf915e8ea61037eb9a7523e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f949b7759404230a5c734e8e5522677488ba4885e5903e1cb6a8f35f5c25f94",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-02-27T18:43:40Z",
    "title_canon_sha256": "ec05be884a5b2feda3f8a4c898b639302d3900622413b99a19f2ffbf3330a886"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.08624",
    "kind": "arxiv",
    "version": 2
  }
}