Pith Number

pith:NQZ6OP6I

pith:2017:NQZ6OP6I6VKIOBSMPOMLN46RYP

not attested not anchored not stored refs pending

Martingale transform and Square function: some weak and restricted weak sharp weighted estimates

Alexander Volberg, Paata Ivanisvili

arxiv:1711.10578 v2 · 2017-11-28 · math.AP · math.CA · 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{NQZ6OP6I6VKIOBSMPOMLN46RYP}

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	2026-05-18T00:19:03.025851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c33e73fc8f55487064c7b98b6f3d1c3f1d1e6be090066f76f7a17719964d286

Aliases

arxiv: 1711.10578 · arxiv_version: 1711.10578v2 · doi: 10.48550/arxiv.1711.10578 · pith_short_12: NQZ6OP6I6VKI · pith_short_16: NQZ6OP6I6VKIOBSM · pith_short_8: NQZ6OP6I

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/NQZ6OP6I6VKIOBSMPOMLN46RYP \
  | 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: 6c33e73fc8f55487064c7b98b6f3d1c3f1d1e6be090066f76f7a17719964d286

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b39dd38a004b337f59f448ce28d5ca581ea5dadc139f64d3d3319be98dda76da",
    "cross_cats_sorted": [
      "math.CA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-11-28T21:54:39Z",
    "title_canon_sha256": "3b8cc707d44e59e24b3849f699c280c9d511ed5a049ab7286bc651a37d8a0dd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.10578",
    "kind": "arxiv",
    "version": 2
  }
}