Pith Number

pith:ST32FQ7W

pith:2011:ST32FQ7WDFBXNUGMPJHPL35RXD

not attested not anchored not stored refs pending

Perturbation of Burkholder's martingale transform and Monge--Amp\`ere equation

Alexander Volberg, Nicholas Boros, Prabhu Janakiraman

arxiv:1102.3905 v1 · 2011-02-18 · math.PR · math.AP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ST32FQ7WDFBXNUGMPJHPL35RXD}

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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	2026-05-18T04:28:20.692598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94f7a2c3f6194376d0cc7a4ef5efb1b8e55418e2e78ff3eaeed15d83bc3e8347

Aliases

arxiv: 1102.3905 · arxiv_version: 1102.3905v1 · doi: 10.48550/arxiv.1102.3905 · pith_short_12: ST32FQ7WDFBX · pith_short_16: ST32FQ7WDFBXNUGM · pith_short_8: ST32FQ7W

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/ST32FQ7WDFBXNUGMPJHPL35RXD \
  | 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: 94f7a2c3f6194376d0cc7a4ef5efb1b8e55418e2e78ff3eaeed15d83bc3e8347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f215e5675068cb36363a50cb7b1d3a26ca0b8c4e9a05ce598e9196ea4db954d2",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-18T20:38:59Z",
    "title_canon_sha256": "ad40830789c4fe845d75801043c692adc1f40b7a82d988ef8fe08fa174fb491e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.3905",
    "kind": "arxiv",
    "version": 1
  }
}