Pith Number

pith:FIDXJ6JL

pith:2010:FIDXJ6JLPUFKWUOHVC6X5RVHLP

not attested not anchored not stored refs pending

Classical Proofs Of Kato Type Smoothing Estimates for The Schr\"odinger Equation with Quadratic Potential in R^n+1 with application

Xuwen Chen

arxiv:1003.4330 v5 · 2010-03-23 · math.AP · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FIDXJ6JLPUFKWUOHVC6X5RVHLP}

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	2026-05-18T04:35:05.048298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a0774f92b7d0aab51c7a8bd7ec6a75bfcc9a1e7b4c6c67cd775194ae3688ac9

Aliases

arxiv: 1003.4330 · arxiv_version: 1003.4330v5 · doi: 10.48550/arxiv.1003.4330 · pith_short_12: FIDXJ6JLPUFK · pith_short_16: FIDXJ6JLPUFKWUOH · pith_short_8: FIDXJ6JL

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/FIDXJ6JLPUFKWUOHVC6X5RVHLP \
  | 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: 2a0774f92b7d0aab51c7a8bd7ec6a75bfcc9a1e7b4c6c67cd775194ae3688ac9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84e7ab9eef55cb4b0e8a2d11f1465a4149ed232c1d94129ea52ea562e4069b56",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-03-23T03:07:33Z",
    "title_canon_sha256": "e5fecffd962552bc8aff3edc91c3559a760e2a26bf41c814655ba9aea7b65775"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.4330",
    "kind": "arxiv",
    "version": 5
  }
}