Pith Number

pith:GP7VUVHL

pith:2023:GP7VUVHLFDK5SCEFBZQNWETOMT

not attested not anchored not stored refs pending

Better than square-root cancellation for random multiplicative functions

Max Wenqiang Xu

arxiv:2303.06774 v2 · 2023-03-12 · math.NT · math.CA · 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{GP7VUVHLFDK5SCEFBZQNWETOMT}

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	2026-07-05T07:05:07.015379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33ff5a54eb28d5d908850e60db126e64dc7ac7cd168c236681ad3003d35c890c

Aliases

arxiv: 2303.06774 · arxiv_version: 2303.06774v2 · doi: 10.48550/arxiv.2303.06774 · pith_short_12: GP7VUVHLFDK5 · pith_short_16: GP7VUVHLFDK5SCEF · pith_short_8: GP7VUVHL

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/GP7VUVHLFDK5SCEFBZQNWETOMT \
  | 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: 33ff5a54eb28d5d908850e60db126e64dc7ac7cd168c236681ad3003d35c890c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c21163d0ca7efa28ffd07484a4c83750185890584d6300f52702ffa817124b62",
    "cross_cats_sorted": [
      "math.CA",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2023-03-12T23:20:11Z",
    "title_canon_sha256": "a335e2fbcc80fc2f5c2f10c38b72c7c3dff6b4a02f687a1fc31ff713486a2228"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.06774",
    "kind": "arxiv",
    "version": 2
  }
}