Pith Number

pith:DCKVMDE6

pith:2015:DCKVMDE6RXOBCFIINILETMXS2R

not attested not anchored not stored refs pending

Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups

Daesung Kim

arxiv:1506.01208 v1 · 2015-06-03 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DCKVMDE6RXOBCFIINILETMXS2R}

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	2026-05-18T01:58:24.823693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1895560c9e8ddc1115086a1649b2f2d4602825ab57c5d97fe6d8a73368d48892

Aliases

arxiv: 1506.01208 · arxiv_version: 1506.01208v1 · doi: 10.48550/arxiv.1506.01208 · pith_short_12: DCKVMDE6RXOB · pith_short_16: DCKVMDE6RXOBCFII · pith_short_8: DCKVMDE6

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/DCKVMDE6RXOBCFIINILETMXS2R \
  | 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: 1895560c9e8ddc1115086a1649b2f2d4602825ab57c5d97fe6d8a73368d48892

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82239ab556f05f08e08aa4ac24094d4dbd9f106fb71fed36d37978fc537e0ba3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-03T11:10:53Z",
    "title_canon_sha256": "a09e630cb81bbd41b3b22f6708227a768fcedba29d785577c4284365fc60ecd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.01208",
    "kind": "arxiv",
    "version": 1
  }
}