Pith Number

pith:OQQYAANP

pith:2015:OQQYAANPPMRXJN5OEXEDNS2L72

not attested not anchored not stored refs pending

Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori

Quanhua Xu, Runlian Xia, Xiao Xiong

arxiv:1507.02409 v3 · 2015-07-09 · math.OA · 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{OQQYAANPPMRXJN5OEXEDNS2L72}

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	2026-05-18T01:22:57.671808Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74218001af7b2374b7ae25c836cb4bfe87b60bf054bfad5eace439ec7c18cd95

Aliases

arxiv: 1507.02409 · arxiv_version: 1507.02409v3 · doi: 10.48550/arxiv.1507.02409 · pith_short_12: OQQYAANPPMRX · pith_short_16: OQQYAANPPMRXJN5O · pith_short_8: OQQYAANP

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/OQQYAANPPMRXJN5OEXEDNS2L72 \
  | 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: 74218001af7b2374b7ae25c836cb4bfe87b60bf054bfad5eace439ec7c18cd95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1700c8115d3e2e2122a8d24736fa3ef6688d71eb0ef45ee79fe34e751612408d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-07-09T08:12:40Z",
    "title_canon_sha256": "de278eddccf9a8125ef9ab5a5ec68bcb477bec3e8feb20e774fc5cfaa39f804e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02409",
    "kind": "arxiv",
    "version": 3
  }
}