Pith Number

pith:52OEAS3X

pith:2015:52OEAS3XH2Z4C6WP5ZKLUXUIAM

not attested not anchored not stored refs pending

Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure

Alexander Volberg, Jonas Azzam, Jos\'e Mar\'ia Martell, Mihalis Mourgoglou, Steve Hofmann, Svitlana Mayboroda, Xavier Tolsa

arxiv:1509.06558 v1 · 2015-09-22 · 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{52OEAS3XH2Z4C6WP5ZKLUXUIAM}

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	2026-05-18T00:03:50.612856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee9c404b773eb3c17acfee54ba5e88030672646fee469fe608d648c06762e696

Aliases

arxiv: 1509.06558 · arxiv_version: 1509.06558v1 · doi: 10.48550/arxiv.1509.06558 · pith_short_12: 52OEAS3XH2Z4 · pith_short_16: 52OEAS3XH2Z4C6WP · pith_short_8: 52OEAS3X

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/52OEAS3XH2Z4C6WP5ZKLUXUIAM \
  | 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: ee9c404b773eb3c17acfee54ba5e88030672646fee469fe608d648c06762e696

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0df266d47d73c75e334cd70c2280e1f238da53be9c299c7bdbe875a0d452ae41",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-22T11:58:41Z",
    "title_canon_sha256": "f190d3c1f46c0e88da2008b04972475f36ac7d3dc6ac6080a12561adfac90d39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06558",
    "kind": "arxiv",
    "version": 1
  }
}