Pith Number

pith:W7SUCXGJ

pith:2017:W7SUCXGJOFGZ4LBB7CDDZOVJMI

not attested not anchored not stored refs pending

Maximal function estimates and self-improvement results for Poincar\'e inequalities

Antti V. V\"ah\"akangas, Juha Kinnunen, Juha Lehrb\"ack, Xiao Zhong

arxiv:1705.05072 v1 · 2017-05-15 · math.CA · 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{W7SUCXGJOFGZ4LBB7CDDZOVJMI}

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	2026-05-18T00:44:32.928613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7e5415cc9714d9e2c21f8863cbaa96209673a372dfff7cd7fd964bad1b14f90

Aliases

arxiv: 1705.05072 · arxiv_version: 1705.05072v1 · doi: 10.48550/arxiv.1705.05072 · pith_short_12: W7SUCXGJOFGZ · pith_short_16: W7SUCXGJOFGZ4LBB · pith_short_8: W7SUCXGJ

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/W7SUCXGJOFGZ4LBB7CDDZOVJMI \
  | 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: b7e5415cc9714d9e2c21f8863cbaa96209673a372dfff7cd7fd964bad1b14f90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c878d13c86f2524a875cd98b6b1a826b79fc066960a41f4686fd6691749a9a0d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-05-15T05:27:25Z",
    "title_canon_sha256": "ea613600330ab903fb173af6bb07a19180f9bfff1d443f5d6ad3434f199cb11c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.05072",
    "kind": "arxiv",
    "version": 1
  }
}