This revision clarifies an essential principle:

Unity does not scale, fail, or restore. Only its differentiated expressions do.

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1. Definition

Unity ((U)) is the ontologically primary condition of being. It is not composed of parts, is not a member of any set, and does not arise from a prior structure. Unity is not numerical oneness but pre‑differentiated coherence—the condition that makes determination, contrast, relation, and intelligibility possible.

Unity is not a container or a totality; it is the condition under which containers, totals, distinctions, and relational structures may arise. Nothing stands outside Unity because exteriority requires differentiation, and differentiation presupposes Unity.

Thus:

• Unity precedes the distinction between the one and the many.
• Unity is not one entity among others, but the enabling field for entities, relations, and Worlds.
• Unity is not shaped, modified, or affected by what arises within it.

Unity is the ground of grounds.

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2. Function / Role

Unity serves as the coherence condition for all structures, ensuring that emergence does not produce ontological fragmentation. Its role is foundational in four respects:

2.1 Ground of Determination

Any differentiation—including polarity (A2)—must occur within a prior undifferentiated ground. Unity enables determinacy by providing the background in which contrast becomes meaningful.

2.2 Ground of Relationality

Relations presuppose a field in which relata are not absolutely separate. Unity accounts for the fact that entities, Worlds, and concepts remain mutually intelligible.

2.3 Ground of Persistence

Persistence across transformations (world transitions, contextual shifts, novelty excursions) is possible only because Unity underwrites identity through change.

2.4 Ground of Integration

Reintegration ((\oplus)) requires a locus of coherence that does not itself fragment. Unity is that locus, enabling novelty to be incorporated without collapse.

Unity’s function is not to unify distinct things, but to ensure that the emergence of distinctions never destroys the intelligibility that makes them possible.

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3. Oppositional Structure

Unity does not form a σ‑pair and possesses no internal poles. It is strictly non‑oppositional:

• not a positive term opposed to a negative,
• not the complement of multiplicity,
• not a counterpart to plurality.

Opposition presupposes distinction; distinction presupposes Unity. Therefore:

• Unity has no σ‑structure.
• σ‑structure has Unity as its necessary ground.

Unity does not stand against polarity; polarity is the first structured expression within Unity.

Unity is “+0”: neither pole, neither axis, neither position.

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4. Scaling Properties

Unity is scale-invariant, not because it exists at all scales, but because it does not participate in scaling at all.

Unity does not scale. Scaling occurs within Unity.

Unity is not:

• enlarged when more systems arise,
• diminished when systems collapse,
• made richer when Worlds proliferate.

Instead:

• individual identity scales within Unity,
• interpersonal meaning scales within Unity,
• social and civilizational structures scale within Unity,
• inter-World mappings occur within Unity.

Unity is the unchanging ontological background that makes scaling possible.

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5. Distortions / Failure Modes

Unity itself does not fail. Failure modes arise only in differentiated expressions of Unity.

6. Restoration Targets

Because Unity cannot fragment or degrade, restoration cannot return to Unity. Restoration restores expressions of Unity, not Unity itself.

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7. Cross-Domain Projections

7.1 Philosophy

Unity corresponds to:

• Taoist Tao (as the source of yin/yang),
• Advaita’s Brahman,
• Nishida’s “place of nothingness,”
• Spinoza’s Substance,
• Whitehead’s Creativity.

UPA’s Unity differs in being structural, not metaphysical or theological.

7.2 Psychology

Unity does not appear as a psychological state.
It appears as the condition that makes any coherent psychological state possible.

Unity is undifferentiated coherence; the precondition for intelligibility. The psyche differentiates into foundational pairs:

• autonomy ↔ belonging
• control ↔ surrender
• self ↔ other
• stability ↔ change
• openness ↔ guardedness
• ideal ↔ actual

7.3 Social and Political Theory

Societies do not possess Unity, but their intelligibility presupposes it.

7.4 SGI / AI

Simulated Unity is the invariant geometric substrate (Sⁿ + σ-pairs + ℓ-levels) that SGI uses to generate semantic polarity axes and Worlds.

8. Summary of Revisions

This revised Axiom 1 now incorporates across all sections as appropriate:

• Unity does not scale.
• Unity does not fail.
• Unity does not restore.
• Scaling, failure, and restoration occur only within differentiated structures (σ‑pairs, Worlds, systems).

Unity remains the inviolable ontological background.

This clarifies the relationship between Unity and all higher axioms and removes any risk of reifying Unity.