Pith Number

pith:J4BZ5FD2

pith:2010:J4BZ5FD2K4FDDW6KIWJY2VLWP6

not attested not anchored not stored refs pending

The Transformation Operator for One-Dimensional Schroedinger Operators on Almost Periodic Infinite-Gap Backgrounds

Katrin Grunert

arxiv:1006.3997 v2 · 2010-06-21 · 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{J4BZ5FD2K4FDDW6KIWJY2VLWP6}

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	2026-05-18T04:25:03.089486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f039e947a570a31dbca45938d55767f8c67d43e86160dbb2fca0f7bc5179007

Aliases

arxiv: 1006.3997 · arxiv_version: 1006.3997v2 · doi: 10.48550/arxiv.1006.3997 · pith_short_12: J4BZ5FD2K4FD · pith_short_16: J4BZ5FD2K4FDDW6K · pith_short_8: J4BZ5FD2

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/J4BZ5FD2K4FDDW6KIWJY2VLWP6 \
  | 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: 4f039e947a570a31dbca45938d55767f8c67d43e86160dbb2fca0f7bc5179007

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1f00bdc8266e2ee7f14c1b01bc73b1ce8216334a42b1811993a7f80a995ef18",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-06-21T06:57:33Z",
    "title_canon_sha256": "655967bd524b56faf7e25aa9f869cfedee7cea665ee1170b5ff0f4eaaf3d0766"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3997",
    "kind": "arxiv",
    "version": 2
  }
}