Pith Number

pith:APH4XKSP

pith:2014:APH4XKSPEDNPP3RXSH6TNCZIU2

not attested not anchored not stored refs pending

Helson's problem for sums of a random multiplicative function

Andriy Bondarenko, Kristian Seip

arxiv:1411.6388 v2 · 2014-11-24 · 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{APH4XKSPEDNPP3RXSH6TNCZIU2}

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	2026-05-18T01:25:02.626661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03cfcbaa4f20daf7ee3791fd368b28a6abd4eefc46b3401d43bfae256b4c04a0

Aliases

arxiv: 1411.6388 · arxiv_version: 1411.6388v2 · doi: 10.48550/arxiv.1411.6388 · pith_short_12: APH4XKSPEDNP · pith_short_16: APH4XKSPEDNPP3RX · pith_short_8: APH4XKSP

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/APH4XKSPEDNPP3RXSH6TNCZIU2 \
  | 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: 03cfcbaa4f20daf7ee3791fd368b28a6abd4eefc46b3401d43bfae256b4c04a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83c8c198a8ded6e2c19bb67df9339f75ac2541aaa47ae0559905bc74593627a4",
    "cross_cats_sorted": [
      "math.CV",
      "math.FA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-11-24T09:15:25Z",
    "title_canon_sha256": "b17265969f958d512c38f7ec976f29671766b40230024581e5d7fb2369847084"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.6388",
    "kind": "arxiv",
    "version": 2
  }
}