Pith Number

pith:FZ5IP7LC

pith:2018:FZ5IP7LC7SDIKFC2ZMRVIZN3TO

not attested not anchored not stored refs pending

Variational estimates for martingale paraproducts

Pavel Zorin-Kranich, Vjekoslav Kova\v{c}

arxiv:1812.09763 v2 · 2018-12-23 · math.PR · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FZ5IP7LC7SDIKFC2ZMRVIZN3TO}

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	2026-07-05T00:04:07.000292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e7a87fd62fc8685145acb235465bb9b81950cfd5fab5db20f1f82bb8751ef5c

Aliases

arxiv: 1812.09763 · arxiv_version: 1812.09763v2 · doi: 10.48550/arxiv.1812.09763 · pith_short_12: FZ5IP7LC7SDI · pith_short_16: FZ5IP7LC7SDIKFC2 · pith_short_8: FZ5IP7LC

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/FZ5IP7LC7SDIKFC2ZMRVIZN3TO \
  | 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: 2e7a87fd62fc8685145acb235465bb9b81950cfd5fab5db20f1f82bb8751ef5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aaaaef56da7b591105ba9216f016dbb886b3420aa65074ff0d6189d8857552a9",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-12-23T19:38:19Z",
    "title_canon_sha256": "6c3dd5ce31c90e74c31923f669a783ed1588ca476a61a8c7eca541c2a7319614"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.09763",
    "kind": "arxiv",
    "version": 2
  }
}