Pith Number

pith:ATTGHNEW

pith:2026:ATTGHNEWXYJKWNESQPBHE7CMVI

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Remarks on generic stability and random types

Karim Khanaki

rgs and irgs for Keisler measures are equivalent to generically stable random type extensions

arxiv:2605.15870 v1 · 2026-05-15 · math.LO

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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

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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

rgs is equivalent to the existence of a generically stable random type extending μ, and irgs to the canonical extension r_μ being generically stable. Every irgs measure is dependent in the sense of [10].

C2weakest assumption

The standard background definitions of Keisler measures, random types, generic stability, and the canonical extension r_μ from model theory literature hold and are applicable here.

C3one line summary

Introduces rgs and irgs for Keisler measures with equivalences to generic stability of random types and proves irgs implies dependence.

References

14 extracted · 14 resolved · 1 Pith anchors

[1] Ben Yaacov,Transfer of properties between measures and random types, Unpublished research note, 2008 2008

[2] I. Ben Yaacov, A. Berenstein, C. W. Henson, and A. Usvyatsov,Model theory for metric structures, inModel Theory with Applications to Al- gebra and Analysis, vol. 2, London Mathematical Society Lecture 2008

[3] Ben Yaacov and H 2009

[4] G. Conant, K. Gannon, and J. Hanson,Keisler measures in the wild, Model Theory, vol. 2, no. 1, pp. 1–67, 2023. doi:10.2140/mt.2023.2.1 2023 · doi:10.2140/mt.2023.2.1

[5] G. Conant, K. Gannon, and J. Hanson,Generic stability, randomiza- tions, and NIP formulas, arXiv preprint arXiv:2308.01801, 2023 2023

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:22.882299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04e663b496be12ab349283c2727c4caa248145549c4f20f58984c687abde8e43

Aliases

arxiv: 2605.15870 · arxiv_version: 2605.15870v1 · doi: 10.48550/arxiv.2605.15870 · pith_short_12: ATTGHNEWXYJK · pith_short_16: ATTGHNEWXYJKWNES · pith_short_8: ATTGHNEW

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/ATTGHNEWXYJKWNESQPBHE7CMVI \
  | 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: 04e663b496be12ab349283c2727c4caa248145549c4f20f58984c687abde8e43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3db340aa142b283ac2cee5d40b41023dce569441000a7fc62875b71a02db3f3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-15T11:39:23Z",
    "title_canon_sha256": "83d61509fc725d12a05cb3cdbc90551d251f93357d3632b8d288f72941b2c90a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15870",
    "kind": "arxiv",
    "version": 1
  }
}