Pith Number

pith:Q336S5PR

pith:2013:Q336S5PRZRJO5VQUGYHNEMD6YM

not attested not anchored not stored refs pending

A note on $k$-hyperreflexivity of Toeplitz-harmonic subspaces

Kamila Piwowarczyk, Marek Ptak, Piotr Budzynski

arxiv:1311.1333 v1 · 2013-11-06 · 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{Q336S5PRZRJO5VQUGYHNEMD6YM}

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	2026-05-18T00:06:31.681568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86f7e975f1cc52eed614360ed2307ec32376834d212bed5cafcffc32b0485a5b

Aliases

arxiv: 1311.1333 · arxiv_version: 1311.1333v1 · doi: 10.48550/arxiv.1311.1333 · pith_short_12: Q336S5PRZRJO · pith_short_16: Q336S5PRZRJO5VQU · pith_short_8: Q336S5PR

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/Q336S5PRZRJO5VQUGYHNEMD6YM \
  | 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: 86f7e975f1cc52eed614360ed2307ec32376834d212bed5cafcffc32b0485a5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e21eb7720094135e5bcd9ec40e9f016a0e72a573737144699bd09e94d64f85f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-11-06T10:06:02Z",
    "title_canon_sha256": "afed97b7b93581a805e84dbe3ccef865afc53343835552cb456a8bd6af409bc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1333",
    "kind": "arxiv",
    "version": 1
  }
}