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modal.html

<!DOCTYPE html>
<html>
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Modal-Abhandlungen – Das Pompeji-Projekt</title>
    <base href="https://pompeji-project.org">
    <link rel="canonical" href="https://pompeji-project.org/modal.html">

    <meta name="description" content="Die modallogischen Abhandlungen (Versionen 1–5 und Module 6–17) – formale Beweise für die Trinität als notwendige Struktur einer monistischen Modalontologie. Mit interaktiven Tutorials.">
    <meta name="robots" content="index, follow">

    <meta property="og:title" content="Modal-Abhandlungen – Das Pompeji-Projekt">
    <meta property="og:description" content="Modallogische Beweise für die Trinität – Versionen 1–5 und Module 6–17 mit Tutorials.">
    <meta property="og:type" content="website">
    <meta property="og:url" content="https://pompeji-project.org/modal.html">
    <meta property="og:locale" content="de_DE">
    <meta property="og:locale:alternate" content="en_US">

    <style>
        * {
            margin: 0;
            padding: 0;
            box-sizing: border-box;
        }

        body {
            font-family: 'Georgia', 'Times New Roman', Times, serif;
            background-color: #f5f3ef;
            color: #2c2c2c;
            line-height: 1.7;
            padding: 2rem 1rem;
        }

        .container {
            max-width: 1000px;
            margin: 0 auto;
            background-color: #fffef7;
            padding: 2rem 2.5rem;
            border-radius: 16px;
            box-shadow: 0 8px 30px rgba(0,0,0,0.08);
            border: 1px solid #e0d6c8;
        }

        /* ===== HEADER ===== */
        .header-row {
            display: flex;
            justify-content: space-between;
            align-items: flex-start;
            flex-wrap: wrap;
            gap: 0.5rem 1rem;
            margin-bottom: 0.3rem;
        }

        .header-left {
            flex: 1;
        }

        .header-left h1 {
            font-size: 2rem;
            font-weight: normal;
            color: #2c2c2c;
            border-left: 6px solid #6b4f8a;
            padding-left: 1rem;
            margin-bottom: 0.2rem;
        }

        .lang-toggle {
            display: flex;
            gap: 0.3rem;
            background-color: #f0ede6;
            padding: 0.2rem;
            border-radius: 30px;
            border: 1px solid #d4cab8;
            flex-shrink: 0;
            margin-top: 0.2rem;
        }

        .lang-toggle button {
            background: none;
            border: none;
            padding: 0.2rem 0.8rem;
            border-radius: 30px;
            font-size: 0.75rem;
            font-family: inherit;
            cursor: pointer;
            color: #8b8b8b;
            transition: background-color 0.2s, color 0.2s;
        }

        .lang-toggle button.active {
            background-color: #6b4f8a;
            color: #fffef7;
        }

        .lang-toggle button:hover:not(.active) {
            background-color: #e0d6c8;
        }

        .back-link {
            display: inline-block;
            margin-bottom: 1.2rem;
            color: #6b4f8a;
            text-decoration: none;
            font-size: 0.9rem;
            border-bottom: 1px solid transparent;
            transition: border-color 0.2s;
        }

        .back-link:hover {
            border-bottom-color: #6b4f8a;
        }

        .subhead {
            font-size: 0.95rem;
            color: #6b6b6b;
            margin-bottom: 2rem;
            border-bottom: 1px solid #e0d6c8;
            padding-bottom: 0.8rem;
        }

        /* ===== LANGUAGE CONTAINERS ===== */
        .lang-de-container {
            display: block;
        }
        .lang-en-container {
            display: none;
        }

        body.lang-en .lang-de-container {
            display: none;
        }
        body.lang-en .lang-en-container {
            display: block;
        }

        /* ===== INTRO ===== */
        .intro-text {
            background-color: #f0ede6;
            padding: 1.5rem 2rem;
            border-radius: 10px;
            margin-bottom: 1.5rem;
            border-left: 4px solid #6b4f8a;
        }

        .intro-text p {
            margin-bottom: 0.8rem;
        }

        .intro-text p:last-child {
            margin-bottom: 0;
        }

        /* ===== ORDNUNG (Entwicklung der Versionen) ===== */
        .reihe-ordnung {
            background-color: #faf8f3;
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        /* ===== TUTORIALS ===== */
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    </style>
</head>
<body>

    <div class="container">

        <!-- ===== BACK LINK ===== -->
        <div class="lang-de-container">
            <a href="./" class="back-link">← Zurück zur Einstiegsseite</a>
        </div>
        <div class="lang-en-container">
            <a href="./" class="back-link">← Back to the entry page</a>
        </div>

        <!-- ===== HEADER ===== -->
        <div class="header-row">
            <div class="header-left">
                <div class="lang-de-container">
                    <h1>📐 Modal-Abhandlungen</h1>
                </div>
                <div class="lang-en-container">
                    <h1>📐 Modal Treatises</h1>
                </div>
            </div>
            <div class="lang-toggle" role="group" aria-label="Sprache umschalten">
                <button id="langDe" class="active" aria-pressed="true">🇩🇪 DE</button>
                <button id="langEn" aria-pressed="false">🇬🇧 EN</button>
            </div>
        </div>

        <div class="subhead">
            <div class="lang-de-container">
                Die Trinität als notwendige Struktur einer monistischen Modalontologie<br>
                <span style="font-size:0.85rem; color:#8b8b8b;">Modallogische Beweisführung – Versionen 1–5 und Module 6–17</span>
            </div>
            <div class="lang-en-container">
                The Trinity as a Necessary Structure of a Monistic Modal Ontology<br>
                <span style="font-size:0.85rem; color:#8b8b8b;">Modal-logical proof – Versions 1–5 and Modules 6–17</span>
            </div>
        </div>

        <!-- ===== INTRO ===== -->
        <div class="intro-text">
            <div class="lang-de-container">
                <p><strong>Was ist das?</strong></p>
                <p>
                    Die <strong>modallogischen Abhandlungen</strong> beweisen formal, dass unter den Axiomen des Monismus,
                    der Existenz einer möglichen Welt und weiterer metaphysischer Annahmen eine <strong>trinitarische Struktur</strong>
                    aus <strong>Ursprung (U)</strong>, <strong>Totalität (T)</strong> und <strong>Selbsterkenntnis (S)</strong>
                    notwendig folgt.
                </p>
                <p>
                    Die Abhandlungen sind <strong>keine Gottesbeweise</strong> im klassischen Sinne. Sie zeigen:
                    <em>Wenn Sie die Axiome akzeptieren, dann folgt die Trinitätsstruktur logisch zwingend.</em>
                </p>
                <p>
                    Die modallogischen Abhandlungen sind der <strong>formale Zugang</strong> zu denselben Fragen,
                    die die Erzählung <em>Die Zeitlosigkeit der Steine</em> narrativ entfaltet. Keiner der beiden
                    Zugänge setzt den anderen voraus.
                </p>
                <p>
                    Die <strong>Module 6–17</strong> erweitern die Untersuchung. Sie sind thematisch in vier Bündeln
                    zusammengefasst: Axiomatik (6–8), Perspektiven (9–11), Konsequenzen (12–14), Grenze (15–17).
                </p>
                <p style="margin-top:0.8rem; font-style:italic; color:#6b4f8a;">
                    📖 Die Versionen 1–5 und die Module 6–17 sind in Deutsch und Englisch verfügbar – als PDF, EPUB, DOCX, TeX und MD.
                </p>
            </div>

            <div class="lang-en-container">
                <p><strong>What is this?</strong></p>
                <p>
                    The <strong>modal-logical treatises</strong> formally prove that under the axioms of monism,
                    the existence of a possible world, and further metaphysical assumptions, a <strong>Trinitarian structure</strong>
                    of <strong>Origin (U)</strong>, <strong>Totality (T)</strong>, and <strong>Self-Knowledge (S)</strong>
                    necessarily follows.
                </p>
                <p>
                    The treatises are <strong>not proofs of God</strong> in the classical sense. They show:
                    <em>If you accept the axioms, then the Trinitarian structure follows logically and necessarily.</em>
                </p>
                <p>
                    The modal-logical treatises are the <strong>formal approach</strong> to the same questions
                    that the narrative <em>The Timelessness of Stones</em> unfolds narratively. Neither approach
                    presupposes the other.
                </p>
                <p>
                    <strong>Modules 6–17</strong> extend the investigation. They are grouped thematically into four
                    bundles: Axiomatics (6–8), Perspectives (9–11), Consequences (12–14), Limit (15–17).
                </p>
                <p style="margin-top:0.8rem; font-style:italic; color:#6b4f8a;">
                    📖 Versions 1–5 and Modules 6–17 are available in German and English – as PDF, EPUB, DOCX, TeX and MD.
                </p>
            </div>
        </div>

        <!-- ===== ORDNUNG DER REIHE ===== -->
        <div class="reihe-ordnung">
            <div class="lang-de-container">
                <p><strong>Die fünf Versionen sind keine Alternativen. Sie sind Stationen einer Entwicklung.</strong></p>
                <p>
                    <strong>Version 1</strong> formuliert den ersten systematischen Versuch: die Trinität aus sechs
                    Axiomen direkt in S5 abzuleiten.
                </p>
                <p>
                    Die <strong>Versionen 2 bis 4</strong> dokumentieren die Zwischenschritte: die Reduktion der Axiome,
                    die Entdeckung der Nicht-Ableitbarkeit in reinem S5, die Einführung der Superpositions-Axiome.
                </p>
                <p>
                    <strong>Version 5</strong> ist die reifste Fassung. Sie zeigt: In reinem S5 ist die Trinität nicht
                    beweisbar. Unter Superpositions-Axiomen ist sie beweisbar. Die Frage der Minimalität bleibt offen.
                    <span class="empfehlung">Empfohlen</span>
                </p>
                <p>
                    Die <strong>Module 6–17</strong> sind keine Versionen, sondern systematisch verschiedene
                    Untersuchungen. Sie bauen auf Version 5 auf und entfalten ihre Konsequenzen. Sie sind in vier
                    thematischen Bündeln zusammengefasst.
                </p>
                <p style="font-style:italic; color:#6b4f8a;">
                    Wer die Position sucht, liest Version 5 und die Module 6–17. Wer den Weg nachvollziehen will, liest alle.
                </p>
            </div>
            <div class="lang-en-container">
                <p><strong>The five versions are not alternatives. They are stations of a development.</strong></p>
                <p>
                    <strong>Version 1</strong> formulates the first systematic attempt: to derive the Trinity from
                    six axioms directly in S5.
                </p>
                <p>
                    <strong>Versions 2 to 4</strong> document the intermediate steps: the reduction of axioms,
                    the discovery of non-derivability in pure S5, the introduction of superposition axioms.
                </p>
                <p>
                    <strong>Version 5</strong> is the most mature version. It shows: In pure S5, the Trinity is not
                    provable. Under superposition axioms, it is provable. The question of minimality remains open.
                    <span class="empfehlung">Recommended</span>
                </p>
                <p>
                    <strong>Modules 6–17</strong> are not versions, but systematically different investigations.
                    They build on Version 5 and unfold its consequences. They are grouped into four thematic bundles.
                </p>
                <p style="font-style:italic; color:#6b4f8a;">
                    Those who seek the position read Version 5 and Modules 6–17. Those who want to follow the path read all of them.
                </p>
            </div>
        </div>

        <!-- ===== VERSIONEN 1–5 ===== -->
        <div class="version-grid">

            <!-- V1 -->
            <div class="version-card">
                <span class="version-badge v1">Version 1</span>
                <div class="lang-de-container">
                    <div class="version-title">Erste systematische Fassung</div>
                    <div class="version-sub">Sechs Axiome – S5-Beweis</div>
                    <div class="version-desc">
                        Der erste systematische Versuch. Zeigt, was aus sechs Axiomen in S5 folgt.
                    </div>
                    <div class="version-hinweis">
                        Die spätere Analyse (Version 4 und 5) zeigt: Aus diesen Axiomen allein ist die Trinität
                        <em>nicht</em> ableitbar. Version 1 markiert den Ausgangspunkt der Entwicklung.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">First Systematic Version</div>
                    <div class="version-sub">Six axioms – S5 proof</div>
                    <div class="version-desc">
                        The first systematic attempt. Shows what follows from six axioms in S5.
                    </div>
                    <div class="version-hinweis">
                        Later analysis (Version 4 and 5) shows: From these axioms alone, the Trinity is
                        <em>not</em> derivable. Version 1 marks the starting point of the development.
                    </div>
                </div>
                <div class="btn-group">
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal.pdf" class="primary">PDF DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modaleng.pdf">PDF EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal.epub">EPUB DE</a>
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                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal.docx">DOCX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modaleng.docx">DOCX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal.tex">TeX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modaleng.tex">TeX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal.md">MD DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modaleng.md">MD EN</a>
                </div>
            </div>

            <!-- V2 -->
            <div class="version-card">
                <span class="version-badge v2">Version 2</span>
                <div class="lang-de-container">
                    <div class="version-title">Minimalistische, grenzwertbasierte Version</div>
                    <div class="version-sub">Zwei Axiome – offenes Intervall</div>
                    <div class="version-desc">
                        Reduktion auf zwei Axiome: Monismus (A1) und Existenz einer möglichen Welt (A4).
                        U, T und S werden als Grenzwerte eines offenen Intervalls verstanden.
                    </div>
                    <div class="version-hinweis">
                        Der Versuch, mit möglichst wenigen Axiomen auszukommen. Die transzendentale Deduktion
                        der weiteren Prinzipien bleibt in dieser Fassung programmatisch.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">Minimalist, Limit-Based Version</div>
                    <div class="version-sub">Two axioms – open interval</div>
                    <div class="version-desc">
                        Reduction to two axioms: Monism (A1) and Existence of a possible world (A4).
                        U, T, and S are understood as limits of an open interval.
                    </div>
                    <div class="version-hinweis">
                        The attempt to get by with as few axioms as possible. The transcendental deduction
                        of further principles remains programmatic in this version.
                    </div>
                </div>
                <div class="btn-group">
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.pdf" class="v2-primary">PDF DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2eng.pdf">PDF EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.epub">EPUB DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2eng.epub">EPUB EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.docx">DOCX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2eng.docx">DOCX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.tex">TeX DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2eng.tex">TeX EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2.md">MD DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal2eng.md">MD EN</a>
                </div>
            </div>

            <!-- V3 -->
            <div class="version-card">
                <span class="version-badge v3">Version 3</span>
                <div class="lang-de-container">
                    <div class="version-title">Fassung mit transzendentalen Brücken</div>
                    <div class="version-sub">Vier Axiome – A11 und A12</div>
                    <div class="version-desc">
                        Ergänzt die Basisaxiome um die transzendentale Brücke (A11) und die Identität von
                        Erfahrbarkeit und Realisierung (A12).
                    </div>
                    <div class="version-hinweis">
                        Diese Fassung präzisiert die Begriffe. Die spätere Analyse (Version 4) zeigt jedoch,
                        dass auch vier Axiome nicht ausreichen, um die Notwendigkeit zu erzwingen.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">Version with Transcendental Bridges</div>
                    <div class="version-sub">Four axioms – A11 and A12</div>
                    <div class="version-desc">
                        Extends the basic axioms by the transcendental bridge (A11) and the identity of
                        experienceability and realization (A12).
                    </div>
                    <div class="version-hinweis">
                        This version sharpens the concepts. However, later analysis (Version 4) shows that
                        even four axioms are not sufficient to enforce necessity.
                    </div>
                </div>
                <div class="btn-group">
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3.pdf" class="v3-primary">PDF DE</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3eng.pdf">PDF EN</a>
                    <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal3.epub">EPUB DE</a>
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                </div>
            </div>

            <!-- V4 -->
            <div class="version-card">
                <span class="version-badge v4">Version 4</span>
                <div class="lang-de-container">
                    <div class="version-title">Vollständige formale Analyse</div>
                    <div class="version-sub">Teil I–III: Nicht-Ableitbarkeit, Beweis, Einordnung</div>
                    <div class="version-desc">
                        Diese Version macht die entscheidende Wende sichtbar: Teil I zeigt die Nicht-Ableitbarkeit
                        in reinem S5. Teil II führt die Superpositions-Axiome ein und beweist die Zielaussage
                        in S5+SP. Teil III ordnet das Ergebnis metalogisch ein.
                    </div>
                    <div class="version-hinweis">
                        Hier wird zum ersten Mal ausgesprochen, was die früheren Versionen verdeckt hatten:
                        Die Trinität folgt nicht aus dem Monismus allein. Sie braucht zusätzliche Struktur.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">Complete Formal Analysis</div>
                    <div class="version-sub">Parts I–III: Non-derivability, Proof, Classification</div>
                    <div class="version-desc">
                        This version makes the decisive turn visible: Part I shows non-derivability in pure S5.
                        Part II introduces superposition axioms and proves the target statement in S5+SP.
                        Part III classifies the result meta-theoretically.
                    </div>
                    <div class="version-hinweis">
                        Here, for the first time, what the earlier versions had concealed is expressed:
                        The Trinity does not follow from monism alone. It needs additional structure.
                    </div>
                </div>
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                </div>
            </div>

            <!-- V5 -->
            <div class="version-card aktuell">
                <span class="empfohlen-badge">Empfohlen</span>
                <span class="version-badge v5">Version 5</span>
                <div class="lang-de-container">
                    <div class="version-title">Reifste Fassung – metalogische Untersuchung</div>
                    <div class="version-sub">Vier Ebenen: Logik, Metaphysik, Physik, Hermeneutik</div>
                    <div class="version-desc">
                        Die reifste Fassung. Sie unterscheidet vier Ebenen der Untersuchung: Logik (Widerspruchsfreiheit),
                        Metaphysik (Strukturbedingungen), Physik (Realisierung) und Theologie/Hermeneutik (Deutung).
                        Die formale Analyse zeigt: Die Trinität folgt nicht aus reinem S5, sondern nur unter
                        Superpositions-Axiomen. Die Frage der Minimalität bleibt offen.
                    </div>
                    <div class="version-hinweis">
                        Wer die Position sucht, liest diese Fassung. Sie ist die einzige, die das Ergebnis
                        der gesamten Entwicklung vollständig ausspricht.
                    </div>
                </div>
                <div class="lang-en-container">
                    <div class="version-title">Most Mature Version – Meta-logical Investigation</div>
                    <div class="version-sub">Four levels: Logic, Metaphysics, Physics, Hermeneutics</div>
                    <div class="version-desc">
                        The most mature version. It distinguishes four levels of investigation: Logic (consistency),
                        Metaphysics (structural conditions), Physics (realization), and Theology/Hermeneutics (interpretation).
                        The formal analysis shows: The Trinity does not follow from pure S5, but only under
                        superposition axioms. The question of minimality remains open.
                    </div>
                    <div class="version-hinweis">
                        Those who seek the position read this version. It is the only one that fully expresses
                        the result of the entire development.
                    </div>
                </div>
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            </div>

        </div>

        <!-- ==================================================================
             MODULE 6–17 – IN VIER BÜNDELN
        =================================================================== -->

        <!-- ===== BÜNDEL 1 ===== -->
        <div class="bundle-section">
            <div class="bundle-header">
                <div class="lang-de-container">
                    <h2>📚 Bündel 1 – Die axiomatische Struktur der Trinität</h2>
                    <p class="bundle-subhead">Module 6–8 · Minimalität, Nicht-Eindeutigkeit, Grenzwert-Modallogik</p>
                </div>
                <div class="lang-en-container">
                    <h2>📚 Bundle 1 – The Axiomatic Structure of the Trinity</h2>
                    <p class="bundle-subhead">Modules 6–8 · Minimality, Non-Uniqueness, Limit Modal Logic</p>
                </div>
            </div>

            <div class="version-grid">

                <!-- Modul 6 -->
                <div class="version-card">
                    <span class="version-badge v1">Modul 6</span>
                    <div class="lang-de-container">
                        <div class="version-title">Die Minimalität der Superpositions-Axiome</div>
                        <div class="version-sub">Eine metalogische Untersuchung zur Unabhängigkeit von ASP1–ASP5</div>
                        <div class="version-desc">
                            Für jedes i ∈ {1,…,5} existiert ein Modell, das ASP1–ASP5 ohne ASP_i erfüllt,
                            aber in dem ¬□∀xTr(x) gilt. Damit ist jedes der fünf Axiome unverzichtbar.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">The Minimality of the Superposition Axioms</div>
                        <div class="version-sub">A Metalogical Investigation into the Independence of ASP1–ASP5</div>
                        <div class="version-desc">
                            For each i ∈ {1,…,5}, there is a model that satisfies ASP1–ASP5 without ASP_i,
                            but in which ¬□∀xTr(x) holds. Hence each of the five axioms is indispensable.
                        </div>
                    </div>
                    <div class="btn-group">
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                    </div>
                </div>

                <!-- Modul 7 -->
                <div class="version-card">
                    <span class="version-badge v2">Modul 7</span>
                    <div class="lang-de-container">
                        <div class="version-title">Die Nicht-Eindeutigkeit der Superpositions-Axiome</div>
                        <div class="version-sub">Drei alternative Erweiterungen von S5</div>
                        <div class="version-desc">
                            Es gibt mindestens vier systematisch verschiedene Erweiterungen von S5,
                            die die Trinität ableiten: Superposition, Topologie, Temporalität, Mereologie.
                            Die Trinität ist axiomen-invariant.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">The Non-Uniqueness of the Superposition Axioms</div>
                        <div class="version-sub">Three Alternative Extensions of S5</div>
                        <div class="version-desc">
                            There are at least four systematically different extensions of S5 that
                            derive the Trinity: superposition, topology, temporality, mereology.
                            The Trinity is axiom-invariant.
                        </div>
                    </div>
                    <div class="btn-group">
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                    </div>
                </div>

                <!-- Modul 8 -->
                <div class="version-card">
                    <span class="version-badge v3">Modul 8</span>
                    <div class="lang-de-container">
                        <div class="version-title">Die Trinität als Grenzwert</div>
                        <div class="version-sub">Topologische Modallogik der monistischen Struktur</div>
                        <div class="version-desc">
                            Die informal gebliebene Grenzwertdefinition aus modal5.md wird präzise gefasst.
                            Der Grenzwertoperator ℒ mit Nachbarschaftssemantik leistet die Übersetzung.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">The Trinity as Limit</div>
                        <div class="version-sub">Topological Modal Logic of the Monistic Structure</div>
                        <div class="version-desc">
                            The limit definition that remained informal in modal5.md is made precise.
                            The limit operator ℒ with neighborhood semantics accomplishes the translation.
                        </div>
                    </div>
                    <div class="btn-group">
                        <a href="https://the-last-freedom.org/Projekt_Pompeji/docs/flreader.php?path=&view=modal8.pdf" class="v3-primary">PDF DE</a>
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                    </div>
                </div>

            </div>
        </div>

        <!-- ===== BÜNDEL 2 ===== -->
        <div class="bundle-section">
            <div class="bundle-header">
                <div class="lang-de-container">
                    <h2>📚 Bündel 2 – Die Trinität in verschiedenen Zugängen</h2>
                    <p class="bundle-subhead">Module 9–11 · Bimodale Nicht-Vereinbarkeit, Unitarität, Temporale Modallogik</p>
                </div>
                <div class="lang-en-container">
                    <h2>📚 Bundle 2 – The Trinity in Different Approaches</h2>
                    <p class="bundle-subhead">Modules 9–11 · Bimodal Non-Compatibility, Unitarity, Temporal Modal Logic</p>
                </div>
            </div>

            <div class="version-grid">

                <!-- Modul 9 -->
                <div class="version-card">
                    <span class="version-badge v1">Modul 9</span>
                    <div class="lang-de-container">
                        <div class="version-title">Zwei Perspektiven, ein Grenzwert</div>
                        <div class="version-sub">Bimodale Nicht-Vereinbarkeit bei DeLillo und Van Dormael</div>
                        <div class="version-desc">
                            DeLillo (Kopenhagen) und Van Dormael (MWI) sind nicht vereinbar,
                            aber gleichzeitig wahr. Der Omega-Punkt ist ein Fixpunkt, kein Zustand.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">Two Perspectives, One Limit</div>
                        <div class="version-sub">Bimodal Non-Compatibility in DeLillo and Van Dormael</div>
                        <div class="version-desc">
                            DeLillo (Copenhagen) and Van Dormael (MWI) are not compatible,
                            but simultaneously true. The Omega Point is a fixed point, not a state.
                        </div>
                    </div>
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                <!-- Modul 10 -->
                <div class="version-card">
                    <span class="version-badge v2">Modul 10</span>
                    <div class="lang-de-container">
                        <div class="version-title">Unitarität als Theorem</div>
                        <div class="version-sub">Modallogik der Informationserhaltung</div>
                        <div class="version-desc">
                            Aus den drei Prinzipien U1–U3 folgt die Auferstehung als Theorem.
                            Die Unitarität ist die Struktur der Totalität T selbst.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">Unitarity as Theorem</div>
                        <div class="version-sub">Modal Logic of Information Conservation</div>
                        <div class="version-desc">
                            From the three principles U1–U3, resurrection follows as a theorem.
                            Unitarity is the structure of Totality T itself.
                        </div>
                    </div>
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                </div>

                <!-- Modul 11 -->
                <div class="version-card">
                    <span class="version-badge v3">Modul 11</span>
                    <div class="lang-de-container">
                        <div class="version-title">Zeitlosigkeit und Gegenwart</div>
                        <div class="version-sub">Temporale Modallogik der Trinität</div>
                        <div class="version-desc">
                            Die vier Zeitmodi P, F, N, Z formalisieren die Unterscheidung zwischen
                            Vergangenheit, Zukunft, Gegenwart und Zeitlosigkeit. Die Trinität ist
                            zeitlos und gegenwärtig.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">Timelessness and Presence</div>
                        <div class="version-sub">Temporal Modal Logic of the Trinity</div>
                        <div class="version-desc">
                            The four time modes P, F, N, Z formalize the distinction between
                            past, future, present, and timelessness. The Trinity is timeless
                            and present.
                        </div>
                    </div>
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            </div>
        </div>

        <!-- ===== BÜNDEL 3 ===== -->
        <div class="bundle-section">
            <div class="bundle-header">
                <div class="lang-de-container">
                    <h2>📚 Bündel 3 – Was folgt aus der Trinität?</h2>
                    <p class="bundle-subhead">Module 12–14 · Das Böse als Weg, Beobachter, Einheit der Perspektiven</p>
                </div>
                <div class="lang-en-container">
                    <h2>📚 Bundle 3 – What Follows from the Trinity?</h2>
                    <p class="bundle-subhead">Modules 12–14 · Evil as Path, Observer, Unity of Perspectives</p>
                </div>
            </div>

            <div class="version-grid">

                <!-- Modul 12 -->
                <div class="version-card">
                    <span class="version-badge v1">Modul 12</span>
                    <div class="lang-de-container">
                        <div class="version-title">Das Böse als Weg zum Guten</div>
                        <div class="version-sub">Modallogik der Evolution</div>
                        <div class="version-desc">
                            Das Böse ist kein zweiter Grenzwert, sondern die unvermeidliche Evolution
                            zum Guten. Es ist genetisch, nicht ontologisch. Am Grenzwert ist es
                            aufgehoben — nicht ausgelöscht, sondern integriert.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">Evil as the Path to the Good</div>
                        <div class="version-sub">Modal Logic of Evolution</div>
                        <div class="version-desc">
                            Evil is not a second limit, but the inevitable evolution toward the Good.
                            It is genetic, not ontological. At the limit, it is sublated — not
                            extinguished, but integrated.
                        </div>
                    </div>
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                </div>

                <!-- Modul 13 -->
                <div class="version-card">
                    <span class="version-badge v2">Modul 13</span>
                    <div class="lang-de-container">
                        <div class="version-title">Der Beobachter in zwei Deutungen</div>
                        <div class="version-sub">Modallogik der Messung bei Kopenhagen und MWI</div>
                        <div class="version-desc">
                            Zwei Beobachter-Operatoren 𝓑_D (konstitutiv) und 𝓑_V (nicht-konstitutiv)
                            führen beide zur Trinität — auf verschiedene Weise. Die Trinität ist
                            beobachterkonzeptions-invariant.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">The Observer in Two Interpretations</div>
                        <div class="version-sub">Modal Logic of Measurement in Copenhagen and MWI</div>
                        <div class="version-desc">
                            Two observer operators 𝓑_D (constitutive) and 𝓑_V (non-constitutive)
                            both lead to the Trinity — in different ways. The Trinity is
                            observer-conception-invariant.
                        </div>
                    </div>
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                <!-- Modul 14 -->
                <div class="version-card">
                    <span class="version-badge v3">Modul 14</span>
                    <div class="lang-de-container">
                        <div class="version-title">Die Einheit der Perspektiven</div>
                        <div class="version-sub">Modallogik der Konvergenz</div>
                        <div class="version-desc">
                            Die Einheit K(U, T, S) folgt direkt aus A1. Sie ist konstitutiv,
                            nicht gestiftet. Der Beobachter ist nicht der Stifter der Einheit,
                            sondern ihr Zeuge.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">The Unity of Perspectives</div>
                        <div class="version-sub">Modal Logic of Convergence</div>
                        <div class="version-desc">
                            The unity K(U, T, S) follows directly from A1. It is constitutive,
                            not founded. The observer is not the founder of unity, but its
                            witness.
                        </div>
                    </div>
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            </div>
        </div>

        <!-- ===== BÜNDEL 4 ===== -->
        <div class="bundle-section">
            <div class="bundle-header">
                <div class="lang-de-container">
                    <h2>📚 Bündel 4 – Die Grenze des Formalen</h2>
                    <p class="bundle-subhead">Module 15–17 · Grenze des Formalen, Wege ohne Omega-Punkt, Das Ganze in einem Gedanken</p>
                </div>
                <div class="lang-en-container">
                    <h2>📚 Bundle 4 – The Limit of the Formal</h2>
                    <p class="bundle-subhead">Modules 15–17 · Limit of the Formal, Paths without Omega Point, The Whole in One Thought</p>
                </div>
            </div>

            <div class="version-grid">

                <!-- Modul 15 -->
                <div class="version-card">
                    <span class="version-badge v1">Modul 15</span>
                    <div class="lang-de-container">
                        <div class="version-title">Die Grenze des Formalen</div>
                        <div class="version-sub">Was Modallogik nicht zeigen kann</div>
                        <div class="version-desc">
                            Drei Ebenen: Beweisen, Nahelegen, Nicht-Erreichen. Die Modallogik kann
                            die Notwendigkeit der Trinität unter Annahmen beweisen, aber sie kann
                            die Wahl der Annahmen nicht rechtfertigen.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">The Limit of the Formal</div>
                        <div class="version-sub">What Modal Logic Cannot Show</div>
                        <div class="version-desc">
                            Three levels: proving, suggesting, not reaching. Modal logic can prove
                            the necessity of the Trinity under assumptions, but it cannot justify
                            the choice of assumptions.
                        </div>
                    </div>
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                <!-- Modul 16 -->
                <div class="version-card">
                    <span class="version-badge v2">Modul 16</span>
                    <div class="lang-de-container">
                        <div class="version-title">Wege ohne Omega-Punkt</div>
                        <div class="version-sub">Strukturelle Integration</div>
                        <div class="version-desc">
                            Wege mit Bewusstsein, die nicht zum Omega-Punkt gelangen, sind
                            strukturell integriert. Die Integration ist kein Ereignis, sondern
                            die Form von T.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">Paths without Omega Point</div>
                        <div class="version-sub">Structural Integration</div>
                        <div class="version-desc">
                            Paths with consciousness that do not reach the Omega Point are
                            structurally integrated. Integration is not an event, but the
                            form of T.
                        </div>
                    </div>
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                </div>

                <!-- Modul 17 -->
                <div class="version-card">
                    <span class="version-badge v3">Modul 17</span>
                    <div class="lang-de-container">
                        <div class="version-title">Das Ganze in einem Gedanken</div>
                        <div class="version-sub">Abschluss der modallogischen Reihe</div>
                        <div class="version-desc">
                            Die Summe aus 17 Modulen. Die Trinität ist die Struktur, die
                            alle Wege umfasst — auch die, die nicht ankommen. Wir stehen
                            am Anfang der Unendlichkeit.
                        </div>
                    </div>
                    <div class="lang-en-container">
                        <div class="version-title">The Whole in One Thought</div>
                        <div class="version-sub">Conclusion of the Modal-Logical Series</div>
                        <div class="version-desc">
                            The sum from 17 modules. The Trinity is the structure that
                            encompasses all paths — including those that do not arrive.
                            We stand at the beginning of infinity.
                        </div>
                    </div>
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            </div>
        </div>

        <!-- ===== TUTORIALS ===== -->
        <div class="tutorial-section">
            <div class="lang-de-container">
                <h3>📖 Interaktive Tutorials</h3>
                <p style="font-size:0.9rem; color:#4a4a4a; margin-bottom:0.5rem;">
                    Die Tutorials führen Schritt für Schritt durch die Beweisführung – mit Erklärungen, Formeln und
                    Verständnisfragen. Ideal für alle, die die Abhandlungen nicht nur lesen, sondern verstehen wollen.
                </p>
            </div>
            <div class="lang-en-container">
                <h3>📖 Interactive Tutorials</h3>
                <p style="font-size:0.9rem; color:#4a4a4a; margin-bottom:0.5rem;">
                    The tutorials guide you step by step through the proof – with explanations, formulas, and
                    comprehension questions. Ideal for anyone who wants to understand the treatises, not just read them.
                </p>
            </div>

            <div class="tutorial-grid">

                <div class="tutorial-card">
                    <div class="tut-title">📐 Version 1</div>
                    <div class="lang-de-container">
                        <div class="tut-desc">Erste systematische Fassung – sechs Axiome, S5-Beweis</div>
                    </div>
                    <div class="lang-en-container">
                        <div class="tut-desc">First systematic version – six axioms, S5 proof</div>
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                        <div class="tut-desc">Minimalistische, grenzwertbasierte Version – zwei Axiome</div>
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                        <div class="tut-desc">Minimalist, limit-based version – two axioms</div>
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                        <div class="tut-desc">Fassung mit transzendentalen Brücken – vier Axiome</div>
                    </div>
                    <div class="lang-en-container">
                        <div class="tut-desc">Version with transcendental bridges – four axioms</div>
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                    <div class="lang-de-container">
                        <div class="tut-desc">Vollständige Analyse – Nicht-Ableitbarkeit + Beweis</div>
                    </div>
                    <div class="lang-en-container">
                        <div class="tut-desc">Complete analysis – Non-derivability + Proof</div>
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                    <div class="lang-de-container">
                        <div class="tut-desc">Reifste Fassung – metalogische Untersuchung</div>
                    </div>
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                        <div class="tut-desc">Most mature version – meta-logical investigation</div>
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            <!-- ===== BÜNDEL-TUTORIALS ===== -->
            <div class="tutorial-subhead">
                <div class="lang-de-container">
                    <h4>📚 Bündel-Tutorials</h4>
                    <p>
                        Die Bündel-Tutorials führen Schritt für Schritt durch die Module 6–17.
                        Jedes Tutorial umfasst drei Teile mit je neun bis zehn Schritten.
                    </p>
                </div>
                <div class="lang-en-container">
                    <h4>📚 Bundle Tutorials</h4>
                    <p>
                        The bundle tutorials guide step by step through Modules 6–17.
                        Each tutorial comprises three parts with nine to ten steps each.
                    </p>
                </div>
            </div>

            <div class="tutorial-grid">

                <div class="tutorial-card">
                    <div class="tut-title">📐 Bündel 1</div>
                    <div class="lang-de-container">
                        <div class="tut-desc">Die axiomatische Struktur der Trinität (Modul 6–8)</div>
                    </div>
                    <div class="lang-en-container">
                        <div class="tut-desc">The Axiomatic Structure of the Trinity (Modules 6–8)</div>
                    </div>
                    <div class="btn-group">
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                    </div>
                </div>

                <div class="tutorial-card">
                    <div class="tut-title">📐 Bündel 2</div>
                    <div class="lang-de-container">
                        <div class="tut-desc">Die Trinität in verschiedenen Zugängen (Modul 9–11)</div>
                    </div>
                    <div class="lang-en-container">
                        <div class="tut-desc">The Trinity in Different Approaches (Modules 9–11)</div>
                    </div>
                    <div class="btn-group">
                        <a href="./bundle2tutorial.html" class="tut-primary">▶️ Tutorial DE</a>
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                    </div>
                </div>

                <div class="tutorial-card">
                    <div class="tut-title">📐 Bündel 3</div>
                    <div class="lang-de-container">
                        <div class="tut-desc">Was folgt aus der Trinität? (Modul 12–14)</div>
                    </div>
                    <div class="lang-en-container">
                        <div class="tut-desc">What Follows from the Trinity? (Modules 12–14)</div>
                    </div>
                    <div class="btn-group">
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                </div>

                <div class="tutorial-card">
                    <div class="tut-title">📐 Bündel 4</div>
                    <div class="lang-de-container">
                        <div class="tut-desc">Die Grenze des Formalen (Modul 15–17)</div>
                    </div>
                    <div class="lang-en-container">
                        <div class="tut-desc">The Limit of the Formal (Modules 15–17)</div>
                    </div>
                    <div class="btn-group">
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                </div>

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        </div>

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