Pith Number

pith:WUM4V56N

pith:2018:WUM4V56NBCIA4JGXW4KFQ4ETS3

not attested not anchored not stored refs pending

The Brown-Halmos theorem for a pair of abstract Hardy spaces

Alexei Karlovich, Eugene Shargorodsky

arxiv:1802.08438 v2 · 2018-02-23 · 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{WUM4V56NBCIA4JGXW4KFQ4ETS3}

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	2026-05-18T00:08:15.367800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b519caf7cd08900e24d7b71458709396d93632d8e60e23c3255d3851fe6a9960

Aliases

arxiv: 1802.08438 · arxiv_version: 1802.08438v2 · doi: 10.48550/arxiv.1802.08438 · pith_short_12: WUM4V56NBCIA · pith_short_16: WUM4V56NBCIA4JGX · pith_short_8: WUM4V56N

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/WUM4V56NBCIA4JGXW4KFQ4ETS3 \
  | 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: b519caf7cd08900e24d7b71458709396d93632d8e60e23c3255d3851fe6a9960

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0b3241962e6c8dba4a6538bc993462e33937a993d78040ef1e49342b2e443a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-02-23T08:25:05Z",
    "title_canon_sha256": "75adbe097f46dd0e3c116c8a0ce36269cf5bbf25b17aedecf824fded90c6cc1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.08438",
    "kind": "arxiv",
    "version": 2
  }
}