Pith Number

pith:NGRC757C

pith:2026:NGRC757C34FCRILSCRHRE533DK

not attested not anchored not stored refs pending

Relative uniform completion of a vector lattice

Eugene Bilokopytov, Vladimir G. Troitsky

The relative uniform completion of a vector lattice X inside a larger uniformly complete Z is the intersection of all uniformly complete sublattices of Z containing X.

arxiv:2601.09015 v2 · 2026-01-13 · math.FA

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\usepackage{pith}
\pithnumber{NGRC757C34FCRILSCRHRE533DK}

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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

✓ Portable graph bundle live · download bundle · merged state

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

If X is a sublattice of a uniformly complete vector lattice Z then X^ru may be viewed as the intersection of all uniformly complete sublattices of Z containing X. X^ru may also be characterized via a universal property: every positive operator from X to a uniformly complete vector lattice extends uniquely to X^ru.

C2weakest assumption

The constructions assume X is a vector lattice that can be embedded as a sublattice into some uniformly complete vector lattice Z, together with the standard definitions of uniform completeness and positive operators.

C3one line summary

Multiple constructions of the relative uniform completion of a vector lattice coincide and it satisfies a universal property for extending positive operators to uniformly complete targets.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:11.364427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69a22ff7e2df0a28a172144f12777b1a9591902a9f214a673669c90be80f16e8

Aliases

arxiv: 2601.09015 · arxiv_version: 2601.09015v2 · doi: 10.48550/arxiv.2601.09015 · pith_short_12: NGRC757C34FC · pith_short_16: NGRC757C34FCRILS · pith_short_8: NGRC757C

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/NGRC757C34FCRILSCRHRE533DK \
  | 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: 69a22ff7e2df0a28a172144f12777b1a9591902a9f214a673669c90be80f16e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4926ab62184440aefa2aa0d5a6a605e07bbf5e01641d33cf0626ecdd869915b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-01-13T22:34:19Z",
    "title_canon_sha256": "9ba6ec7f0ad4d7c2b21224f877d4dc9ed5d3aebabcfa7be133f912f04b157898"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.09015",
    "kind": "arxiv",
    "version": 2
  }
}