Pith Number

pith:MW6YKGHY

pith:2025:MW6YKGHYGKSF5OLSCKM2A4SGQS

not attested not anchored not stored refs pending

It\^o formula for planarly branched rough paths

Nannan Li, Xing Gao

arxiv:2501.11886 v2 · 2025-01-21 · 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{MW6YKGHYGKSF5OLSCKM2A4SGQS}

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.

Cited by

1 paper in Pith

Jump It\^o-type formula with arbitrary regularity

Receipt and verification

First computed	2026-07-05T10:23:28.620441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65bd8518f832a45eb9721299a0724684b6775f33412f7ad5b68e351fd9457c65

Aliases

arxiv: 2501.11886 · arxiv_version: 2501.11886v2 · doi: 10.48550/arxiv.2501.11886 · pith_short_12: MW6YKGHYGKSF · pith_short_16: MW6YKGHYGKSF5OLS · pith_short_8: MW6YKGHY

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/MW6YKGHYGKSF5OLSCKM2A4SGQS \
  | 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: 65bd8518f832a45eb9721299a0724684b6775f33412f7ad5b68e351fd9457c65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d20c663a1fe051ecb9393d6736bb75fbc47680fc1bdbddd46375bbc9377e115f",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-01-21T04:48:04Z",
    "title_canon_sha256": "232ddae485d95530ef026207b7b96f072acf9ba58644ede015b5e0cff7b4b407"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.11886",
    "kind": "arxiv",
    "version": 2
  }
}