Pith Number

pith:4ELOA5LW

pith:2015:4ELOA5LWPNDXKWN2RUY6HAXO76

not attested not anchored not stored refs pending

Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type

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

arxiv:1510.02559 v1 · 2015-10-09 · 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{4ELOA5LWPNDXKWN2RUY6HAXO76}

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	2026-05-18T01:30:42.084966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e116e075767b477559ba8d31e382eeffbd591310a7bcd28d963c6df718767a86

Aliases

arxiv: 1510.02559 · arxiv_version: 1510.02559v1 · doi: 10.48550/arxiv.1510.02559 · pith_short_12: 4ELOA5LWPNDX · pith_short_16: 4ELOA5LWPNDXKWN2 · pith_short_8: 4ELOA5LW

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/4ELOA5LWPNDXKWN2RUY6HAXO76 \
  | 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: e116e075767b477559ba8d31e382eeffbd591310a7bcd28d963c6df718767a86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84568dec6c0135cb9fa8bfe80243a86b44a89968823ff7ff982d0b39069877e6",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-10-09T03:19:00Z",
    "title_canon_sha256": "ca68f8c42e915e17fcb1b4e1ab1ab89fff1412ebf6c64dec2270c672eb6a50d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02559",
    "kind": "arxiv",
    "version": 1
  }
}