Pith Number

pith:XI2QUTNV

pith:2017:XI2QUTNVEG6YORBNOHWIRV3VIG

not attested not anchored not stored refs pending

Moments of random multiplicative functions, I: Low moments, better than squareroot cancellation, and critical multiplicative chaos

Adam J. Harper

arxiv:1703.06654 v1 · 2017-03-20 · math.NT · math.CV · math.FA · 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{XI2QUTNVEG6YORBNOHWIRV3VIG}

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	2026-05-18T00:48:22.108528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba350a4db521bd87442d71ec88d77541a5992f4835702d80e53cd78e9359225f

Aliases

arxiv: 1703.06654 · arxiv_version: 1703.06654v1 · doi: 10.48550/arxiv.1703.06654 · pith_short_12: XI2QUTNVEG6Y · pith_short_16: XI2QUTNVEG6YORBN · pith_short_8: XI2QUTNV

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/XI2QUTNVEG6YORBNOHWIRV3VIG \
  | 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: ba350a4db521bd87442d71ec88d77541a5992f4835702d80e53cd78e9359225f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39cf21713dcc1811471e639b15fa34743872c07b612e9ab30e944775ef698629",
    "cross_cats_sorted": [
      "math.CV",
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-03-20T10:20:02Z",
    "title_canon_sha256": "93f5067aa0f8e789b439f29d5fff026d55ab9a5373e3fc612a2ae2cd094702c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.06654",
    "kind": "arxiv",
    "version": 1
  }
}