Pith Number

pith:4IXAUW75

pith:2011:4IXAUW75KZ2RGWB7SA5UZX3B3U

not attested not anchored not stored refs pending

Astala's conjecture from the point of view of singular integrals on metric spaces

Alexander Volberg

arxiv:1112.6148 v1 · 2011-12-28 · math.AP · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4IXAUW75KZ2RGWB7SA5UZX3B3U}

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	2026-05-18T04:05:36.662956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e22e0a5bfd567513583f903b4cdf61dd18a8a3b855388530dc6825e21691da99

Aliases

arxiv: 1112.6148 · arxiv_version: 1112.6148v1 · doi: 10.48550/arxiv.1112.6148 · pith_short_12: 4IXAUW75KZ2R · pith_short_16: 4IXAUW75KZ2RGWB7 · pith_short_8: 4IXAUW75

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/4IXAUW75KZ2RGWB7SA5UZX3B3U \
  | 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: e22e0a5bfd567513583f903b4cdf61dd18a8a3b855388530dc6825e21691da99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef87b3e9bf073803081dbc6b0c4ed5c9da435c4ce32238df86bd0bb53493d250",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-28T17:07:59Z",
    "title_canon_sha256": "9bffa9333230e7e226540cb7fc34b79a6acc8ecbb83cbb829961f427890f15d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6148",
    "kind": "arxiv",
    "version": 1
  }
}