Pith Number

pith:VABYWBMT

pith:2026:VABYWBMTNRE7ZU5IEN3F6AXWXL

not attested not anchored not stored refs pending

Ergodic Theorems, Almost Invariant Sets, and Values of Averages

Valery V. Ryzhikov

arxiv:2605.30309 v1 · 2026-05-28 · 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{VABYWBMTNRE7ZU5IEN3F6AXWXL}

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	2026-05-29T02:06:15.915649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8038b05936c49fcd3a823765f02f6bacf17a97448591d484c469a2b95294902

Aliases

arxiv: 2605.30309 · arxiv_version: 2605.30309v1 · doi: 10.48550/arxiv.2605.30309 · pith_short_12: VABYWBMTNRE7 · pith_short_16: VABYWBMTNRE7ZU5I · pith_short_8: VABYWBMT

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/VABYWBMTNRE7ZU5IEN3F6AXWXL \
  | 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: a8038b05936c49fcd3a823765f02f6bacf17a97448591d484c469a2b95294902

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7401be3e3d2dbee121ac4f376aa5c23e1d9ec033af6f951e900a3bc76afcebb3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-28T17:52:43Z",
    "title_canon_sha256": "fde5f8df44b1b5733643919874b61e6945d824dd2bed891487bce7be378eef95"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.30309",
    "kind": "arxiv",
    "version": 1
  }
}