Pith Number

pith:F5C6F2CT

pith:2017:F5C6F2CTMEX6U3HAOCGY73AXD3

not attested not anchored not stored refs pending

Two types of Rubio de Francia operators on Triebel--Lizorkin and Besov spaces

Eugenia Malinnikova, Nikolay N. Osipov

arxiv:1705.02228 v1 · 2017-05-05 · 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{F5C6F2CTMEX6U3HAOCGY73AXD3}

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	2026-05-18T00:45:00.352272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f45e2e853612fea6ce0708d8fec171eeee4fa582d8341abad831b8a7f594a13

Aliases

arxiv: 1705.02228 · arxiv_version: 1705.02228v1 · doi: 10.48550/arxiv.1705.02228 · pith_short_12: F5C6F2CTMEX6 · pith_short_16: F5C6F2CTMEX6U3HA · pith_short_8: F5C6F2CT

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/F5C6F2CTMEX6U3HAOCGY73AXD3 \
  | 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: 2f45e2e853612fea6ce0708d8fec171eeee4fa582d8341abad831b8a7f594a13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41cbc3f47f3b998188c36e35fe526ec2de4baa04831c92089f85a34b53dc930b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-05-05T13:50:41Z",
    "title_canon_sha256": "1d4b3873069c3a74636aa95a864023fd3a51db08d2ce8c83b2031bfde14d5c4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.02228",
    "kind": "arxiv",
    "version": 1
  }
}