Pith Number

pith:OOYS2INQ

pith:2012:OOYS2INQSX3R6SRQWU65X6R2NQ

not attested not anchored not stored refs pending

Hardy inequalities in Triebel-Lizorkin spaces

Antti V. V\"ah\"akangas, Lizaveta Ihnatsyeva

arxiv:1209.5840 v1 · 2012-09-26 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OOYS2INQSX3R6SRQWU65X6R2NQ}

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	2026-05-18T03:44:46.191439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73b12d21b095f71f4a30b53ddbfa3a6c3a59740cc81150b0d5b1cecbeacf3bcd

Aliases

arxiv: 1209.5840 · arxiv_version: 1209.5840v1 · doi: 10.48550/arxiv.1209.5840 · pith_short_12: OOYS2INQSX3R · pith_short_16: OOYS2INQSX3R6SRQ · pith_short_8: OOYS2INQ

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/OOYS2INQSX3R6SRQWU65X6R2NQ \
  | 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: 73b12d21b095f71f4a30b53ddbfa3a6c3a59740cc81150b0d5b1cecbeacf3bcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b7e229e2875ac437e0c33976cacdd784aec1f79168a4d39e70077020f923442",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-09-26T06:26:22Z",
    "title_canon_sha256": "fae54a59857a40ab40ce1a7c2afb9bcbff6bbda1bb49f794bf0d77023e35a842"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5840",
    "kind": "arxiv",
    "version": 1
  }
}