Pith Number

pith:DVPZZ32S

pith:2016:DVPZZ32SNTZWP3PFJ7KHSRA4KA

not attested not anchored not stored refs pending

Ergodicity of the Liouville system implies the Chowla conjecture

Nikos Frantzikinakis

arxiv:1611.09338 v4 · 2016-11-28 · math.NT · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DVPZZ32SNTZWP3PFJ7KHSRA4KA}

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	2026-05-18T00:28:16.380277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d5f9cef526cf367ede54fd479441c50354674b0f21ba12355d40e0cd02c86a7

Aliases

arxiv: 1611.09338 · arxiv_version: 1611.09338v4 · doi: 10.48550/arxiv.1611.09338 · pith_short_12: DVPZZ32SNTZW · pith_short_16: DVPZZ32SNTZWP3PF · pith_short_8: DVPZZ32S

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/DVPZZ32SNTZWP3PFJ7KHSRA4KA \
  | 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: 1d5f9cef526cf367ede54fd479441c50354674b0f21ba12355d40e0cd02c86a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54f15e767ffcc6899a3064c50629694a9433f856e402f348f638373d56d9cd07",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-11-28T20:47:42Z",
    "title_canon_sha256": "8cf70c4f6b3120711720a2e3315dadd6e9da9d16516fc7364c74f9f1a77079d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09338",
    "kind": "arxiv",
    "version": 4
  }
}