Pith Number

pith:XH2QBGPX

pith:2026:XH2QBGPXXXNAS7JSUVHVGKNWD5

not attested not anchored not stored refs resolved

Universal homogeneous two-sorted ultrametric spaces

Adam Barto\v{s}, Aleksandra Kwiatkowska, Maciej Malicki, Wies{\l}aw Kubi\'s

Treating ultrametric spaces as two-sorted structures with ordered distances yields a countable homogeneous universal space under distance-carrying embeddings.

arxiv:2605.13608 v1 · 2026-05-13 · math.LO

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\pithnumber{XH2QBGPXXXNAS7JSUVHVGKNWD5}

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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

The class of all finite two-sorted ultrametric spaces with dc-embeddings is Fraïssé, and the limit is the countable rational Urysohn ultrametric space U. The space U is dc-universal for all countable ultrametric spaces, and its Cauchy completion is dc-universal for all separable ultrametric spaces.

C2weakest assumption

That the class of finite two-sorted ultrametric spaces equipped with distance-carrying embeddings satisfies the hereditary, joint embedding, and amalgamation properties required for the Fraïssé theorem to apply.

C3one line summary

The countable rational Urysohn ultrametric space U is the Fraïssé limit of finite two-sorted ultrametric spaces under distance-carrying embeddings and is dc-universal for countable ultrametric spaces, with its completion universal for separable ones.

References

33 extracted · 33 resolved · 1 Pith anchors

[1] A. Bartoš, W. Kubiś , Hereditarily indecomposable continua as generic mathematical structures , Selecta Math. (N.S.) 32 (2026), no. 1, Paper No. 14 2026

[2] A. Bartoš, W. Kubiś, A. Kwiatkowska, M. Malicki , Generic dc-auto\-morphisms of two-sorted ultrametric spaces , preprint, 2026 2026

[3] R. Camerlo, A. Marcone, L. Motto Ros , Isometry groups of Polish ultrametric space , arXiv:2508.08480

[4] On homogeneous ultrametric spaces · arXiv:1509.04346

[5] F. Delon , Espaces ultram\'etriques , J. Symbolic Logic 49 (1984), no. 2, 405--424 1984

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:18.089489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9f50099f7bdda097d32a54f5329b61f7c078ec36ad2a85e71aeb569e5d0f1e5

Aliases

arxiv: 2605.13608 · arxiv_version: 2605.13608v1 · doi: 10.48550/arxiv.2605.13608 · pith_short_12: XH2QBGPXXXNA · pith_short_16: XH2QBGPXXXNAS7JS · pith_short_8: XH2QBGPX

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/XH2QBGPXXXNAS7JSUVHVGKNWD5 \
  | 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: b9f50099f7bdda097d32a54f5329b61f7c078ec36ad2a85e71aeb569e5d0f1e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a7c8d7c931a8a5570fcf80b9dfcfe74eebe5ea6abf7288f3aa7883943c4c036",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-13T14:41:48Z",
    "title_canon_sha256": "e5389a1617b3fc928d4f66713ea083b154ccc1806c107d30ef5897bfb917ac36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13608",
    "kind": "arxiv",
    "version": 1
  }
}