Pith Number

pith:VWKGH2PM

pith:2015:VWKGH2PM67PUINNPL54SSAHPSO

not attested not anchored not stored refs pending

Bilinear Decompositions of Products of Hardy and Lipschitz Spaces Through Wavelets

Dachun Yang, Jun Cao, Luong Dang Ky

arxiv:1510.04384 v3 · 2015-10-15 · math.CA · 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{VWKGH2PM67PUINNPL54SSAHPSO}

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	2026-05-18T01:18:52.436856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad9463e9ecf7df4435af5f792900ef93b2dc748f210d8ce46da6edd7f8e7835f

Aliases

arxiv: 1510.04384 · arxiv_version: 1510.04384v3 · doi: 10.48550/arxiv.1510.04384 · pith_short_12: VWKGH2PM67PU · pith_short_16: VWKGH2PM67PUINNP · pith_short_8: VWKGH2PM

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/VWKGH2PM67PUINNPL54SSAHPSO \
  | 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: ad9463e9ecf7df4435af5f792900ef93b2dc748f210d8ce46da6edd7f8e7835f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fe7af23b177e45dac8039e167fb5862656d51175fba8a0840ab20f1159c7f74",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-10-15T03:02:41Z",
    "title_canon_sha256": "34e05e59548d78cce46eb07c11cf18b84e8d62bac34e205846ace737e5e89600"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.04384",
    "kind": "arxiv",
    "version": 3
  }
}