Pith Number

pith:YW7L7LES

pith:2013:YW7L7LESUWYFTVYGB65HSSNDPZ

not attested not anchored not stored refs pending

Uniform openness of multiplication in Banach spaces $L_p$

Adam Majchrzycki, Filip Strobin, Marek Balcerzak

arxiv:1309.3433 v1 · 2013-09-13 · 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{YW7L7LESUWYFTVYGB65HSSNDPZ}

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	2026-05-18T03:13:22.594622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5bebfac92a5b059d7060fba7949a37e4ec8e945a4d0332f4f890a0990ccbbac

Aliases

arxiv: 1309.3433 · arxiv_version: 1309.3433v1 · doi: 10.48550/arxiv.1309.3433 · pith_short_12: YW7L7LESUWYF · pith_short_16: YW7L7LESUWYFTVYG · pith_short_8: YW7L7LES

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/YW7L7LESUWYFTVYGB65HSSNDPZ \
  | 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: c5bebfac92a5b059d7060fba7949a37e4ec8e945a4d0332f4f890a0990ccbbac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0851ba176c59cf70ec12c8a84b6ec92e4123564975ae35326aae96f46f3185a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-09-13T12:16:46Z",
    "title_canon_sha256": "dc1c90c39bfe78dd2929d1532b6bb6a7aa76a14ae560e3b1e747ec7e8399fc0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3433",
    "kind": "arxiv",
    "version": 1
  }
}