Pith Number

pith:7Z3R6MN6

pith:2020:7Z3R6MN6OYPKZCXJPARG5YGABI

not attested not anchored not stored refs pending

Integral Operators on Fock-Sobolev Spaces via Multipliers on Gauss-Sobolev Spaces

Brett D. Wick, Shengkun Wu

arxiv:2004.05231 v1 · 2020-04-10 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7Z3R6MN6OYPKZCXJPARG5YGABI}

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	2026-07-05T00:54:35.066366Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe771f31be761eac8ae978226ee0c00a31c734d60d23d5a2ac456fc0ed88216d

Aliases

arxiv: 2004.05231 · arxiv_version: 2004.05231v1 · doi: 10.48550/arxiv.2004.05231 · pith_short_12: 7Z3R6MN6OYPK · pith_short_16: 7Z3R6MN6OYPKZCXJ · pith_short_8: 7Z3R6MN6

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/7Z3R6MN6OYPKZCXJPARG5YGABI \
  | 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: fe771f31be761eac8ae978226ee0c00a31c734d60d23d5a2ac456fc0ed88216d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "530ea50920932eec7b6cd813525ad37e331230435ddae0627ee9815654e2b4c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2020-04-10T21:09:52Z",
    "title_canon_sha256": "6e222ae5b938052c3aed8ba9b724c5f585b41d0e891226c9ac878a50af2cd395"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2004.05231",
    "kind": "arxiv",
    "version": 1
  }
}