Pith Number

pith:VYKSMCDJ

pith:2012:VYKSMCDJA2XGOKYGF5JYATQECD

not attested not anchored not stored refs pending

Pointwise products of some Banach function spaces and factorization

Karol Le\'snik, Lech Maligranda, Pawe{\l} Kolwicz

arxiv:1211.3135 v1 · 2012-11-13 · 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{VYKSMCDJA2XGOKYGF5JYATQECD}

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	2026-05-18T03:40:50.785967Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae1526086906ae672b062f53804e0410fd1cf2c568bc3e6fedfefb3049a6f803

Aliases

arxiv: 1211.3135 · arxiv_version: 1211.3135v1 · doi: 10.48550/arxiv.1211.3135 · pith_short_12: VYKSMCDJA2XG · pith_short_16: VYKSMCDJA2XGOKYG · pith_short_8: VYKSMCDJ

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/VYKSMCDJA2XGOKYGF5JYATQECD \
  | 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: ae1526086906ae672b062f53804e0410fd1cf2c568bc3e6fedfefb3049a6f803

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f3ffaa830c3113adb6c42bbc5df57fc44bf654671eaa8806f440cfdb49b49c6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-11-13T21:18:11Z",
    "title_canon_sha256": "c95fdc1ea19140137e8bab9a8154365575ad991cab234e6feb55f4bc9d92161b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3135",
    "kind": "arxiv",
    "version": 1
  }
}