Pith Number

pith:O5PN3IEK

pith:2012:O5PN3IEKH72V7T4LOLNBW2MHD2

not attested not anchored not stored refs pending

Ahlfors-Beurling operator on radial functions

Alexander Volberg

arxiv:1203.2291 v1 · 2012-03-10 · math.CA · math.OC · 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{O5PN3IEKH72V7T4LOLNBW2MHD2}

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	2026-05-18T04:00:25.890610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

775edda08a3ff55fcf8b72da1b69871e9d55fd2af1b32ea723cfe97ee50adfaf

Aliases

arxiv: 1203.2291 · arxiv_version: 1203.2291v1 · doi: 10.48550/arxiv.1203.2291 · pith_short_12: O5PN3IEKH72V · pith_short_16: O5PN3IEKH72V7T4L · pith_short_8: O5PN3IEK

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/O5PN3IEKH72V7T4LOLNBW2MHD2 \
  | 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: 775edda08a3ff55fcf8b72da1b69871e9d55fd2af1b32ea723cfe97ee50adfaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f976d6e6099ffcaeed48ce192f6c6139099bfb4294a9a77936b068320af42d2e",
    "cross_cats_sorted": [
      "math.OC",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-03-10T23:33:37Z",
    "title_canon_sha256": "150a43b6bf30cb74474a687857d7d260d0f6678ae79c08eaf85a961e0504c31c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2291",
    "kind": "arxiv",
    "version": 1
  }
}