Pith Number

pith:G3TPGRNW

pith:2015:G3TPGRNWUO6BRXQ5F66TPWWLDC

not attested not anchored not stored refs pending

Rough Bilinear Singular Integrals

Danqing He, Loukas Grafakos, Petr Honz\'ik

arxiv:1509.06099 v2 · 2015-09-21 · 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{G3TPGRNWUO6BRXQ5F66TPWWLDC}

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	2026-05-18T01:32:20.551386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36e6f345b6a3bc18de1d2fbd37dacb1890fbf91a8952c336cded0383adf6b468

Aliases

arxiv: 1509.06099 · arxiv_version: 1509.06099v2 · doi: 10.48550/arxiv.1509.06099 · pith_short_12: G3TPGRNWUO6B · pith_short_16: G3TPGRNWUO6BRXQ5 · pith_short_8: G3TPGRNW

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/G3TPGRNWUO6BRXQ5F66TPWWLDC \
  | 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: 36e6f345b6a3bc18de1d2fbd37dacb1890fbf91a8952c336cded0383adf6b468

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c9d94450ef7bdbc7e1deb9d7fb4ddf9ab1b606308ea241a3af8cd1bbf260ca0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-21T03:03:38Z",
    "title_canon_sha256": "f0182be347182be8ee75796a6b7ba13e810d4c49b3095902de324573752e4e3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06099",
    "kind": "arxiv",
    "version": 2
  }
}