Pith Number

pith:FMIQNKU2

pith:2020:FMIQNKU2Q7ZY245QIXZFHW2K5M

not attested not anchored not stored refs pending

Rough semimartingales and $p$-variation estimates for martingale transforms

Pavel Zorin-Kranich, Peter Friz

arxiv:2008.08897 v2 · 2020-08-20 · 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{FMIQNKU2Q7ZY245QIXZFHW2K5M}

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	2026-07-05T05:52:49.072782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b1106aa9a87f38d73b045f253db4aeb20c7fcb42d0191dda6085677a4af84cb

Aliases

arxiv: 2008.08897 · arxiv_version: 2008.08897v2 · doi: 10.48550/arxiv.2008.08897 · pith_short_12: FMIQNKU2Q7ZY · pith_short_16: FMIQNKU2Q7ZY245Q · pith_short_8: FMIQNKU2

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/FMIQNKU2Q7ZY245QIXZFHW2K5M \
  | 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: 2b1106aa9a87f38d73b045f253db4aeb20c7fcb42d0191dda6085677a4af84cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d14a2cc0b624fe3ae5b4708a8c7e14914fe7adfe53d35084b40bbfbea347459",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-08-20T11:34:06Z",
    "title_canon_sha256": "77c841d3cad016f2ef3a13c3f2788eb0154979302d33a47ef80e6b133e9974e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2008.08897",
    "kind": "arxiv",
    "version": 2
  }
}