Pith Number

pith:K7OKKUEG

pith:2011:K7OKKUEGIGOVQSUJSXDIN4S2QB

not attested not anchored not stored refs pending

Local Rank of Ergodic Symmetric $n$-Powers does not exceed $n!n^{-n}$

V.V. Ryzhikov

arxiv:1108.5660 v1 · 2011-08-29 · 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{K7OKKUEGIGOVQSUJSXDIN4S2QB}

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	2026-05-18T04:14:37.044790Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57dca55086419d584a8995c686f25a80761a0edd5d8858b0ebe6d7bcc8d2bda0

Aliases

arxiv: 1108.5660 · arxiv_version: 1108.5660v1 · doi: 10.48550/arxiv.1108.5660 · pith_short_12: K7OKKUEGIGOV · pith_short_16: K7OKKUEGIGOVQSUJ · pith_short_8: K7OKKUEG

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/K7OKKUEGIGOVQSUJSXDIN4S2QB \
  | 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: 57dca55086419d584a8995c686f25a80761a0edd5d8858b0ebe6d7bcc8d2bda0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1880f2ea552f5e4036fba5b056e1fa4b56322e87611ec5906b8c347d239cce6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-08-29T17:17:02Z",
    "title_canon_sha256": "ff3a95575c1455608642eddd07b7372f37a974a6957aba464a1b7745befbd940"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5660",
    "kind": "arxiv",
    "version": 1
  }
}