Pith Number

pith:FTYIIZP6

pith:2014:FTYIIZP6AYWPTFA4J2MB5ASW5Y

not attested not anchored not stored refs pending

Characterization of compactness of the commutators of bilinear fractional integral operators

Lucas Chaffee, Rodolfo H. Torres

arxiv:1411.0697 v1 · 2014-11-03 · 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{FTYIIZP6AYWPTFA4J2MB5ASW5Y}

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	2026-05-18T02:38:38.420666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cf08465fe062cf9941c4e981e8256ee03fd740bf16d07106ff0091ebc4e2bf1

Aliases

arxiv: 1411.0697 · arxiv_version: 1411.0697v1 · doi: 10.48550/arxiv.1411.0697 · pith_short_12: FTYIIZP6AYWP · pith_short_16: FTYIIZP6AYWPTFA4 · pith_short_8: FTYIIZP6

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/FTYIIZP6AYWPTFA4J2MB5ASW5Y \
  | 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: 2cf08465fe062cf9941c4e981e8256ee03fd740bf16d07106ff0091ebc4e2bf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25a0a584be03d42dcdc7e8647fb083b2a6b6b317b4839b381b62ba314628a792",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-11-03T21:09:20Z",
    "title_canon_sha256": "2453b9502fa1ee7871f42ae4abc078a03e8ffe895c1af829c8aae9393bd6e0c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.0697",
    "kind": "arxiv",
    "version": 1
  }
}