Pith Number

pith:VKBGSMLO

pith:2015:VKBGSMLOQGHJSTIQBTQOFMLFGZ

not attested not anchored not stored refs pending

Marcinkiewicz-type spectral multipliers on Hardy and Lebesgue spaces on product spaces of homogeneous type

Ji Li, Lesley A. Ward, Lixin Yan, Peng Chen, Xuan Thinh Duong

arxiv:1512.01607 v1 · 2015-12-05 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKBGSMLOQGHJSTIQBTQOFMLFGZ}

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	2026-05-18T01:25:10.819709Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa8269316e818e994d100ce0e2b16536413e734df6672f8a2f80a8866e7ca8b0

Aliases

arxiv: 1512.01607 · arxiv_version: 1512.01607v1 · doi: 10.48550/arxiv.1512.01607 · pith_short_12: VKBGSMLOQGHJ · pith_short_16: VKBGSMLOQGHJSTIQ · pith_short_8: VKBGSMLO

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/VKBGSMLOQGHJSTIQBTQOFMLFGZ \
  | 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: aa8269316e818e994d100ce0e2b16536413e734df6672f8a2f80a8866e7ca8b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "794f3ac264df3c37ce8fa4f09b330573881ae85c5c59df42e9159acb32f46825",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-05T01:02:56Z",
    "title_canon_sha256": "b199dcaf811627f3d3df9207d4d9134cfc25d6f5b021b3fcfa434692391ed232"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01607",
    "kind": "arxiv",
    "version": 1
  }
}