Pith Number

pith:BZ4B6CAK

pith:2010:BZ4B6CAK5ZL7AJTJ4E22TQUDS6

not attested not anchored not stored refs pending

Shapiro's Theorem for subspaces

J. M. Almira, T. Oikhberg

arxiv:1009.5535 v2 · 2010-09-28 · 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{BZ4B6CAK5ZL7AJTJ4E22TQUDS6}

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	2026-05-18T04:14:38.078865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e781f080aee57f02669e135a9c283978dab7c4ed7c5fecd37887533288b517c

Aliases

arxiv: 1009.5535 · arxiv_version: 1009.5535v2 · doi: 10.48550/arxiv.1009.5535 · pith_short_12: BZ4B6CAK5ZL7 · pith_short_16: BZ4B6CAK5ZL7AJTJ · pith_short_8: BZ4B6CAK

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/BZ4B6CAK5ZL7AJTJ4E22TQUDS6 \
  | 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: 0e781f080aee57f02669e135a9c283978dab7c4ed7c5fecd37887533288b517c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e8dcd6e307fe0da1ad444b19d311c0c32a1cdde82f117d7b45431c120ae3106",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-09-28T11:29:01Z",
    "title_canon_sha256": "eab6be69b73a06c1548c1911d349411ee70726ae7fc7d9c4bff6caadf50d19ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5535",
    "kind": "arxiv",
    "version": 2
  }
}