Pith Number

pith:HKZA4PRU

pith:2012:HKZA4PRUPIPEX5B5NXHXBCHQB3

not attested not anchored not stored refs pending

An H1-BMO duality theory for semigroups of operators

Tao Mei

arxiv:1204.5082 v3 · 2012-04-23 · math.CA · math.FA · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HKZA4PRUPIPEX5B5NXHXBCHQB3}

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	2026-05-18T03:56:44.681551Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ab20e3e347a1e4bf43d6dcf7088f00ed1717be76f5d0bf02243d013d4cea8c6

Aliases

arxiv: 1204.5082 · arxiv_version: 1204.5082v3 · doi: 10.48550/arxiv.1204.5082 · pith_short_12: HKZA4PRUPIPE · pith_short_16: HKZA4PRUPIPEX5B5 · pith_short_8: HKZA4PRU

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/HKZA4PRUPIPEX5B5NXHXBCHQB3 \
  | 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: 3ab20e3e347a1e4bf43d6dcf7088f00ed1717be76f5d0bf02243d013d4cea8c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a68ee57baa2ed9963913facddaa1bffe61a29cddd3e3c8ee476639fe886692e2",
    "cross_cats_sorted": [
      "math.FA",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-04-23T15:05:43Z",
    "title_canon_sha256": "f6d4df7a1ea6d009150e449b39c43ebbe5ba7122a15a035636f9c7667a87e01e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5082",
    "kind": "arxiv",
    "version": 3
  }
}