Pith Number

pith:DVPYCFZX

pith:2026:DVPYCFZXM7O4SIU4WTHGCVF5PW

not attested not anchored not stored refs pending

A sharp almost sure upper bound for partial sums of random multiplicative functions

Andrew Pearce-Crump, Benjamin Durkan

arxiv:2607.29429 v1 · 2026-07-31 · 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{DVPYCFZXM7O4SIU4WTHGCVF5PW}

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	2026-08-03T01:34:20.459287Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d5f81173767ddc9229cb4ce6154bd7da810ce555fc7f79e1aa874479588b767

Aliases

arxiv: 2607.29429 · arxiv_version: 2607.29429v1 · doi: 10.48550/arxiv.2607.29429 · pith_short_12: DVPYCFZXM7O4 · pith_short_16: DVPYCFZXM7O4SIU4 · pith_short_8: DVPYCFZX

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/DVPYCFZXM7O4SIU4WTHGCVF5PW \
  | 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: 1d5f81173767ddc9229cb4ce6154bd7da810ce555fc7f79e1aa874479588b767

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fa522d2ecde1b23f6bc4a702093a8bb8e0bddd0303b0b6a621cd7cb527d4646",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-31T13:51:06Z",
    "title_canon_sha256": "1471726dbfc6be46989675f507e6d6213b67996f1143f6efc368a9e77d125c41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29429",
    "kind": "arxiv",
    "version": 1
  }
}