Pith Number

pith:PC7QYY53

pith:2016:PC7QYY537B62MPIXSCBLUXYXCA

not attested not anchored not stored refs pending

Semigroups of composition operators and integral operators on mixed norm spaces

Irina Ar\'evalo, Luis Rodr\'iguez-Piazza, Manuel D. Contreras

arxiv:1610.08784 v1 · 2016-10-27 · math.FA · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PC7QYY537B62MPIXSCBLUXYXCA}

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	2026-05-18T01:01:07.255891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78bf0c63bbf87da63d179082ba5f171026dc85f0c4275110256ac85aa249b402

Aliases

arxiv: 1610.08784 · arxiv_version: 1610.08784v1 · doi: 10.48550/arxiv.1610.08784 · pith_short_12: PC7QYY537B62 · pith_short_16: PC7QYY537B62MPIX · pith_short_8: PC7QYY53

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/PC7QYY537B62MPIXSCBLUXYXCA \
  | 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: 78bf0c63bbf87da63d179082ba5f171026dc85f0c4275110256ac85aa249b402

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5bcc0173af02d0a2b6d18770811cefd7e34ac6794bc31a520f91df841fdea6db",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-10-27T14:01:51Z",
    "title_canon_sha256": "d5150b50c2d6485cc0cc579081e011d288a908a6b3ad84891d49acc225385295"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.08784",
    "kind": "arxiv",
    "version": 1
  }
}