Pith Number

pith:WUG33YQG

pith:2019:WUG33YQGA4ESLECPSGD2EX22JO

not attested not anchored not stored refs pending

The mutual singularity of harmonic measure and Hausdorff measure of codimension smaller than one

Xavier Tolsa

arxiv:1901.07783 v3 · 2019-01-23 · 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{WUG33YQGA4ESLECPSGD2EX22JO}

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	2026-05-17T23:47:43.862344Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b50dbde206070925904f9187a25f5a4b9b0dbdcf326023700b58cc8fc106320f

Aliases

arxiv: 1901.07783 · arxiv_version: 1901.07783v3 · doi: 10.48550/arxiv.1901.07783 · pith_short_12: WUG33YQGA4ES · pith_short_16: WUG33YQGA4ESLECP · pith_short_8: WUG33YQG

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/WUG33YQGA4ESLECPSGD2EX22JO \
  | 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: b50dbde206070925904f9187a25f5a4b9b0dbdcf326023700b58cc8fc106320f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e07e0160e26d3c99097b263ec3444ca5a75dc80abb8831d6b6dcce4b0b49b285",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-01-23T09:34:17Z",
    "title_canon_sha256": "57bca50ba63b95f49ab572b073d89cf771b95b8816fa39ed5198b00222dde402"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.07783",
    "kind": "arxiv",
    "version": 3
  }
}