Pith Number

pith:WP34COMK

pith:2019:WP34COMKUH6XIOJ6KWY2A6NI44

not attested not anchored not stored refs pending

Bochner's Subordionation and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin Spaces

R. Schilling, V. Knopova

arxiv:1908.06786 v3 · 2019-08-19 · math.PR · 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{WP34COMKUH6XIOJ6KWY2A6NI44}

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	2026-07-05T03:48:03.192977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3f7c1398aa1fd74393e55b1a079a8e7337f889597b937baedf5d4f505eaf8d4

Aliases

arxiv: 1908.06786 · arxiv_version: 1908.06786v3 · doi: 10.48550/arxiv.1908.06786 · pith_short_12: WP34COMKUH6X · pith_short_16: WP34COMKUH6XIOJ6 · pith_short_8: WP34COMK

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/WP34COMKUH6XIOJ6KWY2A6NI44 \
  | 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: b3f7c1398aa1fd74393e55b1a079a8e7337f889597b937baedf5d4f505eaf8d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eee8af865a82032536142dcf87f3fe3530a6b4f99390e47f63c445136ddf580c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-08-19T13:21:18Z",
    "title_canon_sha256": "bec18ea3e35d0a29749098c8a1997a096ee6a25a1442ddc53bcd3a578af88bb9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06786",
    "kind": "arxiv",
    "version": 3
  }
}