Pith Number

pith:LEJKL4KY

pith:2017:LEJKL4KYG34JADYUQ4BQWRHNU2

not attested not anchored not stored refs pending

A Liouville theorem for some Bessel generalized operators

Alejandro Quintero, Sandra Molina, Vanesa Galli

arxiv:1708.05758 v2 · 2017-08-18 · 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{LEJKL4KYG34JADYUQ4BQWRHNU2}

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	2026-05-17T23:48:34.559724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5912a5f15836f8900f1487030b44eda6986d5e2a2daeec1e73cb4076ad53e868

Aliases

arxiv: 1708.05758 · arxiv_version: 1708.05758v2 · doi: 10.48550/arxiv.1708.05758 · pith_short_12: LEJKL4KYG34J · pith_short_16: LEJKL4KYG34JADYU · pith_short_8: LEJKL4KY

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/LEJKL4KYG34JADYUQ4BQWRHNU2 \
  | 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: 5912a5f15836f8900f1487030b44eda6986d5e2a2daeec1e73cb4076ad53e868

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2318e324603df9ab9413029a2ef680ed4a0ed8d26ed16222a718028de11f541a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-08-18T20:42:09Z",
    "title_canon_sha256": "a34226615daa99ef3518bea851fcb31fc97592d968e766f3f6cc2f6816cfce93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.05758",
    "kind": "arxiv",
    "version": 2
  }
}