Pith Number

pith:AQ3CSZC7

pith:2026:AQ3CSZC7WQSWW3EBXU3ENJ5GAH

not attested not anchored not stored refs pending

Product sets in sets of returns and positivity of symmetric ergodic averages

Sa\'ul Rodr\'iguez-Mart\'in, Vitaly Bergelson

arxiv:2608.02873 v1 · 2026-08-03 · math.DS · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AQ3CSZC7WQSWW3EBXU3ENJ5GAH}

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	2026-08-05T00:43:12.987071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

043629645fb4256b6c81bd3646a7a601ca10200d55c8df127c3676ea07c09739

Aliases

arxiv: 2608.02873 · arxiv_version: 2608.02873v1 · doi: 10.48550/arxiv.2608.02873 · pith_short_12: AQ3CSZC7WQSW · pith_short_16: AQ3CSZC7WQSWW3EB · pith_short_8: AQ3CSZC7

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/AQ3CSZC7WQSWW3EBXU3ENJ5GAH \
  | 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: 043629645fb4256b6c81bd3646a7a601ca10200d55c8df127c3676ea07c09739

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f2232772f314afcd81e42c88d090998b7d7f83ce1d832e2a97ad8565d47a18a",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-08-03T20:53:48Z",
    "title_canon_sha256": "0dd846cb5263ac8bd35914e893096feedf60afd620391a559a973954e01d1a5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.02873",
    "kind": "arxiv",
    "version": 1
  }
}