Pith Number

pith:BQQO5BJ3

pith:2009:BQQO5BJ3CDQF2YQYWSLCPEKGSR

not attested not anchored not stored refs pending

Properties of Representations of Operators acting between Spaces of Vector-Valued Functions

Delio Mugnolo, Robin Nittka

arxiv:0903.2038 v2 · 2009-03-11 · 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{BQQO5BJ3CDQF2YQYWSLCPEKGSR}

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	2026-05-18T04:23:32.533234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c20ee853b10e05d6218b496279146947be81aa98c628ef6ed0d088937cf02f7

Aliases

arxiv: 0903.2038 · arxiv_version: 0903.2038v2 · doi: 10.48550/arxiv.0903.2038 · pith_short_12: BQQO5BJ3CDQF · pith_short_16: BQQO5BJ3CDQF2YQY · pith_short_8: BQQO5BJ3

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/BQQO5BJ3CDQF2YQYWSLCPEKGSR \
  | 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: 0c20ee853b10e05d6218b496279146947be81aa98c628ef6ed0d088937cf02f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9328ac55d22e80dbf6920d73aa4cfd5a2efb1d57304bde4087d5207128a9b63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-03-11T19:27:13Z",
    "title_canon_sha256": "ea8034d9eb3f54bb49b2ff46dfc04c61e994df3c179552df6cbd0e3386e50857"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.2038",
    "kind": "arxiv",
    "version": 2
  }
}