Pith Number

pith:FKWAH3RV

pith:2013:FKWAH3RVQVZ4YDIAVTXU5TDKG3

not attested not anchored not stored refs pending

Couplings and Strong Approximations to Time Dependent Empirical Processes Based on I.I.D. Fractional Brownian Motions

David M. Mason, P\'eter Kevei

arxiv:1308.4939 v2 · 2013-08-22 · 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{FKWAH3RVQVZ4YDIAVTXU5TDKG3}

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	2026-05-18T01:12:18.933890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2aac03ee358573cc0d00acef4ecc6a36ed2c4573a379f03636230a1bc771c22b

Aliases

arxiv: 1308.4939 · arxiv_version: 1308.4939v2 · doi: 10.48550/arxiv.1308.4939 · pith_short_12: FKWAH3RVQVZ4 · pith_short_16: FKWAH3RVQVZ4YDIA · pith_short_8: FKWAH3RV

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/FKWAH3RVQVZ4YDIAVTXU5TDKG3 \
  | 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: 2aac03ee358573cc0d00acef4ecc6a36ed2c4573a379f03636230a1bc771c22b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1576962cdb0e222e9303817e2d8d7253c4f3baf6885c901b0b4ba3fffa81361",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-08-22T18:14:22Z",
    "title_canon_sha256": "3313ba199211dc9e202bcfa2c26c49c11ebcf96c4c80dfc80ea422f3e07e51af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4939",
    "kind": "arxiv",
    "version": 2
  }
}