Pith Number

pith:WMMQNXOR

pith:2012:WMMQNXORL4X62BUTO2TSBKDORE

not attested not anchored not stored refs pending

Parabolic martingales and non-symmetric Fourier multipliers

Krzysztof Bogdan, {\L}ukasz Wojciechowski

arxiv:1206.0423 v1 · 2012-06-03 · math.FA · 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{WMMQNXORL4X62BUTO2TSBKDORE}

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	2026-05-18T03:54:17.700223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b31906ddd15f2fed069376a720a86e8914b44106be3cc2ca28a955de31c85309

Aliases

arxiv: 1206.0423 · arxiv_version: 1206.0423v1 · doi: 10.48550/arxiv.1206.0423 · pith_short_12: WMMQNXORL4X6 · pith_short_16: WMMQNXORL4X62BUT · pith_short_8: WMMQNXOR

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/WMMQNXORL4X62BUTO2TSBKDORE \
  | 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: b31906ddd15f2fed069376a720a86e8914b44106be3cc2ca28a955de31c85309

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72bda5c58a4d2792e23cfc9471d605c89f560f17e75316f40d3b4e7a62301710",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-06-03T06:10:31Z",
    "title_canon_sha256": "905d44df525052040caa927fbbf4ae6abfa56f3078b039ce5d9bed51e30a4f98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0423",
    "kind": "arxiv",
    "version": 1
  }
}