Pith Number

pith:MHCZH6TE

pith:2015:MHCZH6TEX2IYKCGICCIOAQ3ABM

not attested not anchored not stored refs pending

End-point estimates for singular integrals with non-smooth kernels on product spaces

Ji Li, Lixin Yan, Xuan Thinh Duong

arxiv:1509.07548 v1 · 2015-09-24 · 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{MHCZH6TEX2IYKCGICCIOAQ3ABM}

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	2026-05-18T01:32:02.494796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61c593fa64be918508c81090e043600b1c72fc68dcc93dc552d7b75a76d86911

Aliases

arxiv: 1509.07548 · arxiv_version: 1509.07548v1 · doi: 10.48550/arxiv.1509.07548 · pith_short_12: MHCZH6TEX2IY · pith_short_16: MHCZH6TEX2IYKCGI · pith_short_8: MHCZH6TE

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/MHCZH6TEX2IYKCGICCIOAQ3ABM \
  | 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: 61c593fa64be918508c81090e043600b1c72fc68dcc93dc552d7b75a76d86911

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcdc1fb9ba08e66afac131eaf4ace585a4f2417fb36582b298e96b8e2ff71ce5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-24T22:02:49Z",
    "title_canon_sha256": "957cfa35cbcefd54caed01fe9152fe40dcb6e57c977a1d5f717000b003a3b649"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07548",
    "kind": "arxiv",
    "version": 1
  }
}