Pith Number

pith:22DYHNYC

pith:2026:22DYHNYCETTQM5S7KDIMYZGZSF

not attested not anchored not stored refs pending

Relative uniform convergence and Archimedean property in pre-ordered vector spaces

Eduard Emelyanov

Quotienting a pre-ordered vector space by the intersection of the ru-closure of its positive wedge with the negative produces an Archimedeanization.

arxiv:2602.16419 v7 · 2026-02-18 · math.FA

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\usepackage{pith}
\pithnumber{22DYHNYCETTQM5S7KDIMYZGZSF}

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Record completeness

1 Bitcoin timestamp

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

It is proved that, for a pre-ordered vector space X, the quotient space (X/A,[W]) is an Archimedeanization of X, where W is the closure of the positive wedge X+ in ru-topology, A=W∩(-W), and [W] is the quotient set of W in X/A.

C2weakest assumption

The relative uniform topology is well-defined on the pre-ordered space and the closure W forms a wedge such that the quotient order is compatible and Archimedean.

C3one line summary

For a pre-ordered vector space X, the quotient (X/A, [W]) with W the ru-closure of X+ and A = W ∩ (-W) is an Archimedeanization of X.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-22T02:04:39.980955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d68783b70224e706765f50d0cc64d9916574f65d04bb374ccfbe3cd45a5bef25

Aliases

arxiv: 2602.16419 · arxiv_version: 2602.16419v7 · doi: 10.48550/arxiv.2602.16419 · pith_short_12: 22DYHNYCETTQ · pith_short_16: 22DYHNYCETTQM5S7 · pith_short_8: 22DYHNYC

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/22DYHNYCETTQM5S7KDIMYZGZSF \
  | 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: d68783b70224e706765f50d0cc64d9916574f65d04bb374ccfbe3cd45a5bef25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05e13e6cb8b72f369ba4c759281e1fc2717e9fa7366a82b5e6d9fb2e809a9100",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-02-18T12:49:47Z",
    "title_canon_sha256": "af0d7ad67166da9006b7dafe77a6068f60c282b9ba2933f15bd4d6896dd88871"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.16419",
    "kind": "arxiv",
    "version": 7
  }
}