Pith Number

pith:JZMUMXVG

pith:2024:JZMUMXVGSC73MMW2CT53NSSJYN

not attested not anchored not stored refs pending

Martingale central limit theorem for random multiplicative functions

Mo Dick Wong, Ofir Gorodetsky

arxiv:2405.20311 v2 · 2024-05-30 · math.NT · 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{JZMUMXVGSC73MMW2CT53NSSJYN}

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

2 papers in Pith

Distribution of random multiplicative functions in short intervals, with proper normalization

A few notes on the asymptotic behavior of Rademacher random multiplicative functions

Receipt and verification

First computed	2026-07-05T08:28:10.633897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e59465ea690bfb632da14fbb6ca49c37ed904d7ed62ea6db69c94bd5e0b5403

Aliases

arxiv: 2405.20311 · arxiv_version: 2405.20311v2 · doi: 10.48550/arxiv.2405.20311 · pith_short_12: JZMUMXVGSC73 · pith_short_16: JZMUMXVGSC73MMW2 · pith_short_8: JZMUMXVG

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/JZMUMXVGSC73MMW2CT53NSSJYN \
  | 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: 4e59465ea690bfb632da14fbb6ca49c37ed904d7ed62ea6db69c94bd5e0b5403

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e510710e7d3624e4040a2332bda2ef0706847a52da7a15515e1741cebaa20432",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-05-30T17:53:05Z",
    "title_canon_sha256": "4a0a24f821b2b619533b1e93b4d3190b5790092dcc04c16f19ecce536313bb37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.20311",
    "kind": "arxiv",
    "version": 2
  }
}