Pith Number

pith:RLL5NXXZ

pith:2025:RLL5NXXZCRF7X2PMLOGSOTANOH

not attested not anchored not stored refs pending

Trace definability I: preservation and characterizations

Erik Walsberg

Trace definability is a weakening of definability under which some classification-theoretic properties are preserved and can be characterized.

arxiv:2504.05566 v3 · 2025-04-07 · math.LO

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\usepackage{pith}
\pithnumber{RLL5NXXZCRF7X2PMLOGSOTANOH}

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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

Various classification-theoretic properties are or are not preserved under trace definability, and the properties which are preserved can also be characterized in terms of it.

C2weakest assumption

The introduced notion of trace definability is a coherent and useful weakening of ordinary definability that interacts meaningfully with the classification-theoretic properties under consideration.

C3one line summary

Introduces trace definability for first-order structures and establishes preservation and characterization results for classification-theoretic properties under it.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:10:29.614885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ad7d6def9144bfbe9ec5b8d274c0d71fedabb1deb2136ed5430f9b5a66495df

Aliases

arxiv: 2504.05566 · arxiv_version: 2504.05566v3 · doi: 10.48550/arxiv.2504.05566 · pith_short_12: RLL5NXXZCRF7 · pith_short_16: RLL5NXXZCRF7X2PM · pith_short_8: RLL5NXXZ

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/RLL5NXXZCRF7X2PMLOGSOTANOH \
  | 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: 8ad7d6def9144bfbe9ec5b8d274c0d71fedabb1deb2136ed5430f9b5a66495df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0362f554974111a5ab1e5a8b74fe7bc27abdb0bf9d7895a9efee96d51afd661",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2025-04-07T23:47:12Z",
    "title_canon_sha256": "42e1783b530b860632fcb75fda79f51fa994de47311e2b67b93145a2ca943435"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.05566",
    "kind": "arxiv",
    "version": 3
  }
}