Pith Number

pith:UEEJTJTW

pith:2019:UEEJTJTWRHCUU5HKFCASSEUJXL

not attested not anchored not stored refs pending

The optimal range of the Calder\`{o}n operator and its applications

D. Zanin, F. Sukochev, K. Tulenov

arxiv:1908.09548 v1 · 2019-08-26 · 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{UEEJTJTWRHCUU5HKFCASSEUJXL}

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	2026-07-04T23:59:41.441356Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a10899a67689c54a74ea2881291289bafc54f6d2b3a8ba18c04fac1c3cb55d1c

Aliases

arxiv: 1908.09548 · arxiv_version: 1908.09548v1 · doi: 10.48550/arxiv.1908.09548 · pith_short_12: UEEJTJTWRHCU · pith_short_16: UEEJTJTWRHCUU5HK · pith_short_8: UEEJTJTW

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/UEEJTJTWRHCUU5HKFCASSEUJXL \
  | 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: a10899a67689c54a74ea2881291289bafc54f6d2b3a8ba18c04fac1c3cb55d1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e178739a3996efbb9f59ecb2e672f60584c26320a7c7b04a2aa644dd2640c204",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-08-26T09:18:56Z",
    "title_canon_sha256": "e36849bfbf942d8856351a70160e5fefd3f15fb9f21e319c388387b5ee68b592"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09548",
    "kind": "arxiv",
    "version": 1
  }
}