Pith Number

pith:PKHPA3MN

pith:2015:PKHPA3MNVHI3ESRMH744BJOCSP

not attested not anchored not stored refs pending

$T1$ criterions for generalised Calder\'on--Zygmund type operators on Hardy and BMO spaces associated to Schr\"odinger operators and applications

Fu Ken Ly, Ji Li, The Anh Bui

arxiv:1510.02531 v1 · 2015-10-09 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PKHPA3MNVHI3ESRMH744BJOCSP}

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	2026-05-18T01:30:42.170798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a8ef06d8da9d1b24a2c3ff9c0a5c293d14fa7ddc926a626bbe2d5677ab633f5

Aliases

arxiv: 1510.02531 · arxiv_version: 1510.02531v1 · doi: 10.48550/arxiv.1510.02531 · pith_short_12: PKHPA3MNVHI3 · pith_short_16: PKHPA3MNVHI3ESRM · pith_short_8: PKHPA3MN

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/PKHPA3MNVHI3ESRMH744BJOCSP \
  | 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: 7a8ef06d8da9d1b24a2c3ff9c0a5c293d14fa7ddc926a626bbe2d5677ab633f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83832879bb8a89df26a1918f3c136ef3e96d7eb90e760df0b9c0268d5e79a9c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-09T00:01:27Z",
    "title_canon_sha256": "3ee0784b675a8433b088eea8c54a7879699f15d4559c8642d9dc980708bf3eee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02531",
    "kind": "arxiv",
    "version": 1
  }
}