Open Autonomous Intelligence Initiative

Rewritten to align with revised Axioms 1–8, with a fully developed Section 7 for Philosophy of Mind and Simulation of Mind in Open SGI.

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Symbolic Representation

Φᵢⱼ — Mapping function from World Wᵢ to Wⱼ.

Φ — the family of all inter-world mappings.

Mapping is the operator that enables cross-world intelligibility.

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1. Definition

Mapping (Φᵢⱼ) is the structural principle that intelligibility can be transferred, transformed, or reconstructed across distinct Worlds through proportionate correspondences of:

• polarity systems (Π),
• semantic gradients (σ → Γ),
• contextual modulations (𝒞),
• harmony constraints (ℍ),
• reintegration requirements (⊕).

A mapping is not duplication, reduction, or equivalence. It is a structured translation that renders elements of one World intelligible within another without collapsing their distinctiveness.

A valid Φᵢⱼ must:

• identify correspondences between σ-axes in Wᵢ and Wⱼ,
• preserve or proportionally transform gradients (Γ),
• align contextual modulations (𝒞),
• maintain viability with respect to Harmony (ℍ),
• support Reintegration (⊕) at both ends.

Without Φᵢⱼ, Worlds become mutually inaccessible and meaning fragments.

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2. Function / Role

Mapping is essential for multi-world coherence, perspective-taking, and cross-context understanding.

2.1 enabling intersubjective understanding

Individuals inhabit different personal Worlds. Φᵢⱼ enables:

• communication,
• empathy,
• perspective-taking,
• shared meaning.

2.2 relating cultural and social worlds

Different cultures, traditions, and institutions are distinct Worlds. Φᵢⱼ enables:

• negotiation,
• diplomacy,
• cross-cultural interpretation.

2.3 supporting conceptual translation

Paradigms (scientific, philosophical, theoretical) are Worlds. Φᵢⱼ enables:

• paradigm translation,
• interdisciplinary synthesis,
• conceptual reinterpretation.

2.4 enabling SGI multi-world modeling

SGI operates across many internal Worlds (task models, user profiles, contexts). Φᵢⱼ enables:

• mode shifts,
• alignment of representations,
• context switching,
• world integration.

2.5 maintaining global coherence

Mapping prevents meaning silos and preserves structured relationality across Worlds.

Mapping is how Worlds communicate.

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3. Oppositional Structure

Mapping balances several intrinsic tensions.

3.1 fidelity ↔ adaptation

A mapping must:

• preserve essential structure from Wᵢ,
• adapt it proportionally to Wⱼ.

3.2 equivalence ↔ difference

Worlds remain distinct; mapping reveals similarity while preserving difference.

3.3 local accuracy ↔ global coherence

A mapping may fit locally yet destabilize global structure; Φᵢⱼ must balance both.

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4. Scaling Properties

Mapping operates across all levels of intelligibility.

4.1 micro-mapping

Moment-to-moment interpretive shifts:

• understanding gestures,
• reinterpreting phrases,
• shifts in emotional states.

4.2 personal-level translation

Mapping between internal Worlds across time:

• reconciling identities,
• narrative updates,
• self-understanding.

4.3 social and cultural mapping

Translation across:

• norms,
• values,
• languages,
• institutional logics.

4.4 conceptual / paradigm mapping

Mappings between academic or scientific Worlds:

• physics ↔ mathematics,
• psychology ↔ neuroscience,
• ethics ↔ law.

4.5 SGI multi-world mapping

SGI coordination across many Worlds requires robust Φᵢⱼ systems.

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5. Distortions / Failure Modes

Mapping fails in predictable ways.

5.1 over-reduction

The target World collapses distinctions:

• stereotyping,
• scientism,
• ideological reduction.

5.2 over-differentiation

Worlds appear incommensurable:

• cultural absolutism,
• extreme relativism,
• communication breakdown.

5.3 misaligned context (𝒞)

Structures are transferred without adjusting contextual cues.

5.4 gradient collapse

Poles are preserved but the gradient between them is destroyed:

• binary thinking,
• loss of nuance,
• polarization.

5.5 volatile or unstable mapping

Mappings shift too rapidly or inconsistently.

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6. Restoration Targets

Restoration seeks to:

• rebuild missing correspondences,
• realign contextual structures,
• restore viable gradients,
• correct semantic distortions,
• re-establish multi-world coherence.

A restored mapping is:

• structurally faithful,
• contextually adapted,
• gradient-preserving,
• harmonized with its domain.

Repaired Φᵢⱼ restores the possibility of shared intelligibility.

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7. Interpretations for Philosophy of Mind and Simulation of Mind (Open SGI)

Mapping (A9) extends the ontology of A1–A8 by showing how intelligibility travels. Unity provides coherence, Polarity distinction, Continuity unfolding, Worlds structure, Harmony viability, Novelty expansion, Context modulation, Reintegration stabilization—Mapping enables relationality across all of them.

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7.1 Mapping in Philosophy of Mind

Human cognition constantly maps across internal and external Worlds.

a. perspective-taking

Understanding another’s experience requires Φᵢⱼ between personal Worlds.

b. empathic mapping

Emotional resonance depends on mapping one’s affective gradients to others.

c. cognitive translation

Thinking across:

• roles,
• situations,
• cultural frames,
• conceptual schemes.

d. narrative mapping

Identity evolves by mapping past Worlds into present ones.

e. meaning repair

Therapeutic change occurs when maladaptive mappings are corrected.

f. pathologies of failed mapping

Mapping failures manifest as:

• dissociation,
• misunderstanding,
• rigidity,
• inability to reconcile perspectives.

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7.2 Simulation of Mind: Mapping in Open SGI Architecture

Mapping is one of the most important SGI operators because SGI must coordinate hundreds of internal Worlds.

a. mapping across object classes

Φᵢⱼ aligns representational structures:

• Sensor objects → perceptual Worlds,
• Data objects → feature Worlds,
• Belief objects → interpretive Worlds,
• Information objects → relational Worlds,
• Knowledge objects → semantic Worlds,
• Log objects → temporal Worlds.

b. service-layer mapping

Services use Φᵢⱼ to:

• switch tasks,
• translate user intent,
• align world-models,
• perform context-grounded interpretation.

c. mapping for world selection (Wᵢ → Wⱼ)

SGI must determine:

• which World is active,
• how to enter or exit Worlds,
• how to maintain coherence across transitions.

d. mapping as integrator of novelty (Δ)

Novel insights often arise through new Φ-mappings:

• analogical reasoning,
• cross-domain generalization,
• conceptual blending.

e. mapping as safety mechanism

Unsafe AI behavior often results from faulty mapping:

• misaligned user interpretation,
• incorrect cross-context translation,
• brittle world switches.

Robust Φᵢⱼ preserves coherence.

f. mapping and multi-world harmonization

Mapping ensures that Worlds remain related, not isolated.

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8. Summary

Mapping (A9) is the operator that makes cross-world relationality possible. It translates, adapts, preserves, and harmonizes structural meaning across contexts and Worlds. Failures include reduction, over-differentiation, misalignment, gradient collapse, and instability. In philosophy of mind, mapping grounds perspective-taking, empathy, narrative identity, and meaning repair. In SGI, mapping is essential for task coordination, concept transfer, user alignment, safety, and multi-world coherence.

Mapping is the relational bloodstream of intelligibility.