Pith Number

pith:ABAFFS76

pith:2013:ABAFFS765JKPSMNWE4TKJCL3QH

not attested not anchored not stored refs pending

On the continuity of Fourier multipliers on the homogeneous Sobolev spaces $\dot{W}^1_1(R^d)$

Krystian Kazaniecki, Micha{\l} Wojciechowski

arxiv:1306.1437 v4 · 2013-06-06 · 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{ABAFFS765JKPSMNWE4TKJCL3QH}

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	2026-05-17T23:52:24.930445Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

004052cbfeea54f931b62726a4897b81e27916f0123eaf0707a28615d0403bcd

Aliases

arxiv: 1306.1437 · arxiv_version: 1306.1437v4 · doi: 10.48550/arxiv.1306.1437 · pith_short_12: ABAFFS765JKP · pith_short_16: ABAFFS765JKPSMNW · pith_short_8: ABAFFS76

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/ABAFFS765JKPSMNWE4TKJCL3QH \
  | 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: 004052cbfeea54f931b62726a4897b81e27916f0123eaf0707a28615d0403bcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bffd8fbb049a6b4549c73f919569320564fbb32ba80cef187882c606c6f82fdf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-06-06T15:28:44Z",
    "title_canon_sha256": "293aa0499764938ffc32aecb73ac557d254742ebe6720958748343d7bed621dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1437",
    "kind": "arxiv",
    "version": 4
  }
}