Pith Number

pith:NLHYNUFJ

pith:2025:NLHYNUFJGOZTOG2TO5UJMBKHHT

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Semitopological Barycentric Algebras

Jean Goubault-Larrecq

Free semitopological cones exist over barycentric algebras, along with a general theorem for barycenters of continuous valuations.

arxiv:2512.12865 v4 · 2025-12-14 · math.FA · cs.LO

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Claims

C1strongest claim

We show the existence of free semitopological cones over semitopological barycentric algebras and over pointed semitopological algebras, we investigate which semitopological barycentric algebras embed into semitopological cones and which pointed semitopological barycentric algebras embed strictly into semitopological cones. [...] We conclude with a general barycenter existence theorem, whose proof relies on the study of the Smyth poweralgebra.

C2weakest assumption

The structures satisfy the defining equations of barycentric algebras and carry topologies compatible with the algebraic operations, as assumed throughout the development of semitopological and topological variants.

C3one line summary

Semitopological barycentric algebras admit free semitopological cone constructions and support a general barycenter existence theorem for continuous valuations via the Smyth poweralgebra.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T01:03:52.268161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6acf86d0a933b3371b5377689605473ce496a1bc968b5f343136206f7dce2db4

Aliases

arxiv: 2512.12865 · arxiv_version: 2512.12865v4 · doi: 10.48550/arxiv.2512.12865 · pith_short_12: NLHYNUFJGOZT · pith_short_16: NLHYNUFJGOZTOG2T · pith_short_8: NLHYNUFJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NLHYNUFJGOZTOG2TO5UJMBKHHT \
  | 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: 6acf86d0a933b3371b5377689605473ce496a1bc968b5f343136206f7dce2db4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc984fa662613e8476fdfc10ba3a8aeb5ad1cceeadb3997d9b45781242abc53c",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-12-14T22:46:43Z",
    "title_canon_sha256": "0c3c8fefa8b7331058c6f656956104b8dde67ec5583a5c52922719ef73ee8e06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.12865",
    "kind": "arxiv",
    "version": 4
  }
}