Pith Number

pith:ABLBVCT2

pith:2026:ABLBVCT2OKPYYNH373LCVEGT6P

not attested not anchored not stored refs pending

Invariant random compacts

Bryna Kra, Scott Schmieding

Continuous actions on compact metric spaces can be IC-rigid, forcing every invariant random compact to be almost surely finite or the entire space.

arxiv:2605.03993 v2 · 2026-05-05 · math.DS

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\usepackage{pith}
\pithnumber{ABLBVCT2OKPYYNH373LCVEGT6P}

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Record completeness

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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.

Claims

C1strongest claim

We give sufficient conditions for an action to be IC-rigid, and show there are natural examples of such actions. We further consider a notion of weak IC-rigidity, and prove that the Chacon system is weakly IC-rigid but not IC-rigid. As an application, we prove results concerning multiplicative largeness of dilations of sets on the circle.

C2weakest assumption

The setup assumes X is a compact metric space and the G-action is continuous, which permits the space of nonempty compact subsets to carry a natural topology and invariant measures; additionally, the specific dynamical properties of the Chacon system must distinguish weak from full rigidity.

C3one line summary

Group actions on compact metric spaces are IC-rigid under stated conditions, with the Chacon system weakly IC-rigid, yielding results on multiplicative largeness of dilated sets.

Receipt and verification

First computed	2026-05-29T01:05:11.586467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00561a8a7a729f8c34fbfed62a90d3f3dccb0cbc9f9e15634ea7269062fc2318

Aliases

arxiv: 2605.03993 · arxiv_version: 2605.03993v2 · doi: 10.48550/arxiv.2605.03993 · pith_short_12: ABLBVCT2OKPY · pith_short_16: ABLBVCT2OKPYYNH3 · pith_short_8: ABLBVCT2

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/ABLBVCT2OKPYYNH373LCVEGT6P \
  | 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: 00561a8a7a729f8c34fbfed62a90d3f3dccb0cbc9f9e15634ea7269062fc2318

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a73ef91641360fa81cfdc610574f563974ea6a06ede48c41cb73c4868ef1411",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-05T17:13:37Z",
    "title_canon_sha256": "c2e2954bd0d93ef1d8197a35187ee95469f9bc36250c4e1c6ca50eac689f6987"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03993",
    "kind": "arxiv",
    "version": 2
  }
}