Pith Number

pith:3Q2JYZNN

pith:2024:3Q2JYZNNTOMNFBKI7ZLFFNOZZL

not attested not anchored not stored refs pending

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$

Bingyao Wu, Jie-Xiang Zhu

arxiv:2411.15724 v1 · 2024-11-24 · 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{3Q2JYZNNTOMNFBKI7ZLFFNOZZL}

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	2026-07-05T09:39:40.004478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc349c65ad9b98d28548fe5652b5d9cafff1c12147a30d7a134d4daa5d4447c0

Aliases

arxiv: 2411.15724 · arxiv_version: 2411.15724v1 · doi: 10.48550/arxiv.2411.15724 · pith_short_12: 3Q2JYZNNTOMN · pith_short_16: 3Q2JYZNNTOMNFBKI · pith_short_8: 3Q2JYZNN

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/3Q2JYZNNTOMNFBKI7ZLFFNOZZL \
  | 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: dc349c65ad9b98d28548fe5652b5d9cafff1c12147a30d7a134d4daa5d4447c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "215a947c25350ade0e33ea639e81acc639c96c11887f52a2cc4cc6acb4e97592",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-11-24T06:02:30Z",
    "title_canon_sha256": "71445787d6f2db3586be88677dbe7e1e1f525f600ceaba97e64d95cfec97843f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.15724",
    "kind": "arxiv",
    "version": 1
  }
}