Pith Number

pith:D6OLW6CF

pith:2017:D6OLW6CFBDRFSCV2VPLE2FNTKE

not attested not anchored not stored refs pending

Mixed weak estimates of Sawyer type for fractional integrals and some related operators

Fabio Berra, Gladis Pradolini, Marilina Carena

arxiv:1712.08186 v1 · 2017-12-21 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D6OLW6CFBDRFSCV2VPLE2FNTKE}

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	2026-05-18T00:27:24.223697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f9cbb784508e2590abaabd64d15b351376837d6d24eefcbe92edff148ea952a

Aliases

arxiv: 1712.08186 · arxiv_version: 1712.08186v1 · doi: 10.48550/arxiv.1712.08186 · pith_short_12: D6OLW6CFBDRF · pith_short_16: D6OLW6CFBDRFSCV2 · pith_short_8: D6OLW6CF

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/D6OLW6CFBDRFSCV2VPLE2FNTKE \
  | 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: 1f9cbb784508e2590abaabd64d15b351376837d6d24eefcbe92edff148ea952a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbc13a1c8317451c4c3599e7c966fd247e4d85a788a57458ec473a6132070841",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-12-21T19:31:48Z",
    "title_canon_sha256": "8e91b8501c7de7386add48c6172457e206a76ee3c0d8c28b62762d6bcce05d53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.08186",
    "kind": "arxiv",
    "version": 1
  }
}