Pith Number

pith:77A7ZWJZ

pith:2013:77A7ZWJZIWWHASS4LJCWRQPQWM

not attested not anchored not stored refs pending

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

Helge Krueger

arxiv:1304.2805 v1 · 2013-04-09 · 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{77A7ZWJZIWWHASS4LJCWRQPQWM}

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	2026-05-18T03:28:28.187052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffc1fcd93945ac704a5c5a4568c1f0b314bb8b9415d3f514dddfd1ace0976f50

Aliases

arxiv: 1304.2805 · arxiv_version: 1304.2805v1 · doi: 10.48550/arxiv.1304.2805 · pith_short_12: 77A7ZWJZIWWH · pith_short_16: 77A7ZWJZIWWHASS4 · pith_short_8: 77A7ZWJZ

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/77A7ZWJZIWWHASS4LJCWRQPQWM \
  | 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: ffc1fcd93945ac704a5c5a4568c1f0b314bb8b9415d3f514dddfd1ace0976f50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4937f0ec789b8baf78bcadda5c6175e2170b536876ebb7a2af35d9c657935081",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-04-09T22:09:37Z",
    "title_canon_sha256": "b323ffe5c3e16536232f598783c9bdb21a3ca3d4cb6aa624e8c567e878f1320e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.2805",
    "kind": "arxiv",
    "version": 1
  }
}