Pith Number

pith:T56RN3EY

pith:2019:T56RN3EYL3RUU5NIWD7QOJE44I

not attested not anchored not stored refs pending

The $L^{p}$ boundedness of the wave operators for matrix Schr\"{o}dinger equations

Ricardo Weder

arxiv:1912.12793 v3 · 2019-12-30 · 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{T56RN3EYL3RUU5NIWD7QOJE44I}

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	2026-07-05T03:02:06.949943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f7d16ec985ee34a75a8b0ff07249ce206970f650429314e501a1fc302068bb6

Aliases

arxiv: 1912.12793 · arxiv_version: 1912.12793v3 · doi: 10.48550/arxiv.1912.12793 · pith_short_12: T56RN3EYL3RU · pith_short_16: T56RN3EYL3RUU5NI · pith_short_8: T56RN3EY

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/T56RN3EYL3RUU5NIWD7QOJE44I \
  | 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: 9f7d16ec985ee34a75a8b0ff07249ce206970f650429314e501a1fc302068bb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "898e31255c8f9438b275da4dd8f5fae9747a234e73b404ce8c727f48d1fc9de4",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-12-30T03:05:06Z",
    "title_canon_sha256": "debef226f0c457c711bf1c06b035488ac97b8caabd7a13f218bdc7d4a0d77ea2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.12793",
    "kind": "arxiv",
    "version": 3
  }
}