Pith Number

pith:XNKB4UQ6

pith:2021:XNKB4UQ6WH6EWZCQ7TA55EZNAB

not attested not anchored not stored refs pending

Optimal convergence rates in the averaging principle for slow-fast SPDEs driven by multiplicative noise

Xiaobin Sun, Yi Ge, Yingchao Xie

arxiv:2101.09076 v2 · 2021-01-22 · 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{XNKB4UQ6WH6EWZCQ7TA55EZNAB}

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	2026-07-05T02:44:05.143946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb541e521eb1fc4b6450fcc1de932d00749f5681784454aa7e7c3a64b6073b3a

Aliases

arxiv: 2101.09076 · arxiv_version: 2101.09076v2 · doi: 10.48550/arxiv.2101.09076 · pith_short_12: XNKB4UQ6WH6E · pith_short_16: XNKB4UQ6WH6EWZCQ · pith_short_8: XNKB4UQ6

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/XNKB4UQ6WH6EWZCQ7TA55EZNAB \
  | 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: bb541e521eb1fc4b6450fcc1de932d00749f5681784454aa7e7c3a64b6073b3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1f70b73ef2411065d5b167e8eb5fd6d5c432c0b25dc3c006235fc7cdfa5eb75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-01-22T12:23:10Z",
    "title_canon_sha256": "9abd7bdf158cce996d0b4b6e9d0450b5118b0c251156c99e2f873d0a6460de81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.09076",
    "kind": "arxiv",
    "version": 2
  }
}