Pith Number

pith:SLV6QXZQ

pith:2026:SLV6QXZQ4ZBKPBEYX4NBZAZ7PR

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Pseudo-Complex Quantifier Elimination

Nicolas Faro{\ss}, Thomas Sturm

Quantifier elimination for the complex numbers reduces to real quantifier elimination followed by heuristic reinterpretation in a language with imaginary unit, real parts, imaginary parts, and conjugates.

arxiv:2604.26400 v2 · 2026-04-29 · cs.SC · cs.LO

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\usepackage{pith}
\pithnumber{SLV6QXZQ4ZBKPBEYX4NBZAZ7PR}

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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 describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a reduction to real quantifier elimination followed by a heuristic reinterpretation of the results within our complex framework.

C2weakest assumption

The heuristic reinterpretation step correctly and completely maps results from real quantifier elimination back into the pseudo-complex language without introducing errors or incompleteness.

C3one line summary

A quantifier elimination framework for complex numbers is designed via reduction to real QE followed by heuristic reinterpretation, with examples in the Logic1 system.

Receipt and verification

First computed	2026-06-12T01:09:28.117915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92ebe85f30e642a78498bf1a1c833f7c5bcf8d8e00ae6cfa916d333bee991135

Aliases

arxiv: 2604.26400 · arxiv_version: 2604.26400v2 · doi: 10.48550/arxiv.2604.26400 · pith_short_12: SLV6QXZQ4ZBK · pith_short_16: SLV6QXZQ4ZBKPBEY · pith_short_8: SLV6QXZQ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SLV6QXZQ4ZBKPBEYX4NBZAZ7PR \
  | 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: 92ebe85f30e642a78498bf1a1c833f7c5bcf8d8e00ae6cfa916d333bee991135

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5b72b04270d0621ca510135a445ed4042f1b85a32e01b550c86c95d37977084",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SC",
    "submitted_at": "2026-04-29T08:10:17Z",
    "title_canon_sha256": "ecb40f45c99a91134019441f90fc3d582e6c1dccf247ee2be018a651eaa8499e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26400",
    "kind": "arxiv",
    "version": 2
  }
}