Pith Number

pith:7ISMYQKG

pith:2026:7ISMYQKGLUA462KHD6P2TYTYJL

not attested not anchored not stored refs pending

Structure of 2-step nilpotent ergodic averages for distinct-degree polynomials

Andreas Koutsogiannis, Borys Kuca, Wenbo Sun

arxiv:2607.29368 v1 · 2026-07-31 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ISMYQKGLUA462KHD6P2TYTYJL}

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	2026-08-03T01:33:21.463799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa24cc41465d01cf69471f9fa9e2784af910e4a4600d72761ca5601a3a0eed0c

Aliases

arxiv: 2607.29368 · arxiv_version: 2607.29368v1 · doi: 10.48550/arxiv.2607.29368 · pith_short_12: 7ISMYQKGLUA4 · pith_short_16: 7ISMYQKGLUA462KH · pith_short_8: 7ISMYQKG

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/7ISMYQKGLUA462KHD6P2TYTYJL \
  | 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: fa24cc41465d01cf69471f9fa9e2784af910e4a4600d72761ca5601a3a0eed0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1f43ae5830730ca57732eabb1d712bee2d5bbc521a89e43dbfd4fbb2585da9d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-07-31T12:52:49Z",
    "title_canon_sha256": "87f9ed6d3a2af11346b398f9974d7aa107cddfc21c8518d457b422ad721b2a14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29368",
    "kind": "arxiv",
    "version": 1
  }
}