Pith Number

pith:VIPN4HT2

pith:2013:VIPN4HT2ON52NCEUK43GH2ZUUX

not attested not anchored not stored refs pending

Absolutely continuous spectrum for quasi-periodic Schr\"odinger operators

Helge Krueger

arxiv:1306.4395 v1 · 2013-06-18 · 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{VIPN4HT2ON52NCEUK43GH2ZUUX}

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	2026-05-18T03:20:34.608233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa1ede1e7a737ba68894573663eb34a5fbacd0150b9f5010574c336c368268d7

Aliases

arxiv: 1306.4395 · arxiv_version: 1306.4395v1 · doi: 10.48550/arxiv.1306.4395 · pith_short_12: VIPN4HT2ON52 · pith_short_16: VIPN4HT2ON52NCEU · pith_short_8: VIPN4HT2

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/VIPN4HT2ON52NCEUK43GH2ZUUX \
  | 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: aa1ede1e7a737ba68894573663eb34a5fbacd0150b9f5010574c336c368268d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba2879240c6dfd60a2018dca4be2a729e88d5d33fbf833946aaf0aeac8547b2e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-06-18T23:55:47Z",
    "title_canon_sha256": "6fd1f07210524e71babefda7defa1817c86d7268ca010a23b3f92ff90997377e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.4395",
    "kind": "arxiv",
    "version": 1
  }
}