Pith Number

pith:PPIRB3ZJ

pith:2011:PPIRB3ZJHXNFJG2EGEM5JHDX2T

not attested not anchored not stored refs pending

An infinite-dimensional generalization of Zenger's lemma

Roman Drnov\v{s}ek

arxiv:1111.2734 v1 · 2011-11-11 · 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{PPIRB3ZJHXNFJG2EGEM5JHDX2T}

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	2026-05-18T01:09:25.182340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bd110ef293dda549b443119d49c77d4ce99c506b1c33b91abb82b914d1d2aa6

Aliases

arxiv: 1111.2734 · arxiv_version: 1111.2734v1 · doi: 10.48550/arxiv.1111.2734 · pith_short_12: PPIRB3ZJHXNF · pith_short_16: PPIRB3ZJHXNFJG2E · pith_short_8: PPIRB3ZJ

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/PPIRB3ZJHXNFJG2EGEM5JHDX2T \
  | 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: 7bd110ef293dda549b443119d49c77d4ce99c506b1c33b91abb82b914d1d2aa6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd31fa5fc8c9c348217248a6decbe449cdaa12280c585f1c949540cce0c528bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-11-11T13:14:07Z",
    "title_canon_sha256": "ad96678c27fd7b0018295c32d58d6d2182be9d1a2588a4ee88818ac7052a1d38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2734",
    "kind": "arxiv",
    "version": 1
  }
}