Pith Number

pith:BRFK7CL4

pith:2011:BRFK7CL45KVZ4Z2LDIADMQH375

not attested not anchored not stored refs pending

Endpoint Estimates for N-dimensional Hardy Operators and Their Commutators

Fayou Zhao, Shanzhen Lu, Zunwei Fu

arxiv:1106.0456 v1 · 2011-06-02 · math.FA

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

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	2026-05-18T00:24:10.745355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c4aaf897ceaab9e674b1a003640fbff517a11aec1e8602821725eac1d2dc2ce

Aliases

arxiv: 1106.0456 · arxiv_version: 1106.0456v1 · doi: 10.48550/arxiv.1106.0456 · pith_short_12: BRFK7CL45KVZ · pith_short_16: BRFK7CL45KVZ4Z2L · pith_short_8: BRFK7CL4

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/BRFK7CL45KVZ4Z2LDIADMQH375 \
  | 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: 0c4aaf897ceaab9e674b1a003640fbff517a11aec1e8602821725eac1d2dc2ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2fd3b80f07781ebf16c7e640db5f72248b40670956333d44840ad18e92cd039",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-06-02T15:44:04Z",
    "title_canon_sha256": "5b6f1b5b44d56ae85dcb26f45ca52f931a3bc0cfeb206f32fe57f0f275b06a36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0456",
    "kind": "arxiv",
    "version": 1
  }
}