Pith Number

pith:PHCY5GPH

pith:2018:PHCY5GPHSXJNSDKKFD67NTE6WP

not attested not anchored not stored refs pending

Sobolev-Type Inequalities for Dunkl Operators

Andrei Velicu

arxiv:1811.11118 v2 · 2018-11-27 · 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{PHCY5GPHSXJNSDKKFD67NTE6WP}

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	2026-05-17T23:50:58.800994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79c58e99e795d2d90d4a28fdf6cc9eb3ca1762785a23ccf3355ca883f31fefc3

Aliases

arxiv: 1811.11118 · arxiv_version: 1811.11118v2 · doi: 10.48550/arxiv.1811.11118 · pith_short_12: PHCY5GPHSXJN · pith_short_16: PHCY5GPHSXJNSDKK · pith_short_8: PHCY5GPH

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/PHCY5GPHSXJNSDKKFD67NTE6WP \
  | 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: 79c58e99e795d2d90d4a28fdf6cc9eb3ca1762785a23ccf3355ca883f31fefc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8f3310f90ccbeb3cfcf21df37fc2921fe6678111c142dd8bc305e1de416de73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-11-27T17:30:43Z",
    "title_canon_sha256": "9d31dd2de95e24fe7e966dc26878951390fe5508d7a9947360a2577377902785"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.11118",
    "kind": "arxiv",
    "version": 2
  }
}