Pith Number

pith:4WQRP5XO

pith:2026:4WQRP5XORUJEUBPFMQPFSISXGK

not attested not anchored not stored refs resolved

NTP2 topological structures

Pablo and\'ujar Guerrero

NTP2 expansions of the reals by constructible sets define only constructible sets.

arxiv:2604.24522 v1 · 2026-04-27 · math.LO

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\usepackage{pith}
\pithnumber{4WQRP5XORUJEUBPFMQPFSISXGK}

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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

We prove that every NTP₂ expansion of (ℝ,<,+) by constructible sets defines only constructible sets, and that definable functions are generically piecewise continuous. The result also holds for all NTP₂ expansions of (ℚ_p,+,·), and all NTP₂ definably complete expansions of ordered groups.

C2weakest assumption

The expansions are NTP2 and the added predicates are constructible sets; the proofs rely on this tameness assumption to conclude that definable sets remain constructible.

C3one line summary

NTP2 expansions of (R,<,+) by constructible sets define only constructible sets with generically piecewise continuous functions, with extensions to Qp and ordered groups.

References

3 extracted · 2 resolved · 0 Pith anchors

[1] [FS10] Antongiulio Fornasiero and Tamara Servi

[2] A note on topological model theory.Fund 1973

[3] [Wal22] Erik Walsberg 1910

Receipt and verification

First computed	2026-05-20T14:03:27.074612Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5a117f6ee8d124a05e5641e59225732af0144f1f15635ad4a2f48714a5f34c2

Aliases

arxiv: 2604.24522 · arxiv_version: 2604.24522v1 · doi: 10.48550/arxiv.2604.24522 · pith_short_12: 4WQRP5XORUJE · pith_short_16: 4WQRP5XORUJEUBPF · pith_short_8: 4WQRP5XO

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/4WQRP5XORUJEUBPFMQPFSISXGK \
  | 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: e5a117f6ee8d124a05e5641e59225732af0144f1f15635ad4a2f48714a5f34c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15088ea4e625e78c33543cd8745feecaf748148fa25b8e576b60563e5c98ba49",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-04-27T14:24:17Z",
    "title_canon_sha256": "514e18642eaf5072692c9f0eac36707a19e76c40985ab9d91446af2f311ff621"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24522",
    "kind": "arxiv",
    "version": 1
  }
}