Pith Number

pith:Q72JXD4E

pith:2015:Q72JXD4ESJAN4ZUOZSH4CY2VNZ

not attested not anchored not stored refs pending

Carl's inequality for quasi-Banach spaces

Aicke Hinrichs, Anton Kolleck, Jan Vybiral

arxiv:1512.04421 v2 · 2015-12-14 · 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{Q72JXD4ESJAN4ZUOZSH4CY2VNZ}

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	2026-05-18T01:14:17.546579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87f49b8f849240de668ecc8fc163556e79c05077a9e6e4875a213122fb503fb9

Aliases

arxiv: 1512.04421 · arxiv_version: 1512.04421v2 · doi: 10.48550/arxiv.1512.04421 · pith_short_12: Q72JXD4ESJAN · pith_short_16: Q72JXD4ESJAN4ZUO · pith_short_8: Q72JXD4E

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/Q72JXD4ESJAN4ZUOZSH4CY2VNZ \
  | 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: 87f49b8f849240de668ecc8fc163556e79c05077a9e6e4875a213122fb503fb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da0d6673d6ca018c55b69e861e8bd295c8d622e6419454ffd163494ff64500a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-12-14T17:38:48Z",
    "title_canon_sha256": "5bce5d8ee130a9d3b324391554e6d17e2403761b9b3cec47e13d4a4627f7b680"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04421",
    "kind": "arxiv",
    "version": 2
  }
}