Pith Number

pith:67CA6RTC

pith:2015:67CA6RTCCSE6Q4X47P7EHU2B6M

not attested not anchored not stored refs pending

Harmonic measure and Riesz transform in uniform and general domains

Mihalis Mourgoglou, Xavier Tolsa

arxiv:1509.08386 v3 · 2015-09-28 · math.CA · 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{67CA6RTCCSE6Q4X47P7EHU2B6M}

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	2026-05-18T01:10:20.245723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7c40f46621489e872fcfbfe43d341f307e5259b941a338acd4daf165c228ab6

Aliases

arxiv: 1509.08386 · arxiv_version: 1509.08386v3 · doi: 10.48550/arxiv.1509.08386 · pith_short_12: 67CA6RTCCSE6 · pith_short_16: 67CA6RTCCSE6Q4X4 · pith_short_8: 67CA6RTC

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/67CA6RTCCSE6Q4X47P7EHU2B6M \
  | 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: f7c40f46621489e872fcfbfe43d341f307e5259b941a338acd4daf165c228ab6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ade0469310943d319a3f343cda9cee15a19b9ff9c0591e78c7a25686584eecd2",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-28T16:48:25Z",
    "title_canon_sha256": "49ac227f99302d1409d17d0e418b4531dcf64883bbbef8b3251297fb8ea08eb0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08386",
    "kind": "arxiv",
    "version": 3
  }
}