Consciousness

This document presents the UCF/GUTT understanding of consciousness aligned with formally verified proofs in the Coq proof assistant. The key insight, established in Experience_Is_Relating.v and supporting files, is that experience is not PRODUCED BY relational dynamics—it IS what relating is, from the participant's position. This structural identity dissolves traditional problems while preserving the mathematical machinery for measuring experiential richness.

Every claim in this document maps to one or more formally verified proof files. The mappings are provided inline and summarized at the end.

The formal proof establishes a structural isomorphism:

R(source, target) ≅ Experience(subject, content)

This is not an analogy. The structures are mathematically identical. Source maps to subject. Target maps to content. Directedness maps to intentionality. The proof demonstrates bijection with round-trip preservation—they are the same structure described in different vocabularies.

Proof file: Experience_Is_Relating.v

• Theorem experience_relation_isomorphism: Bijection between structures
• Theorem experience_relation_round_trip: Round-trip preservation
• Theorem hard_problem_dissolved: Category error established

From Proposition 1, everything relates to the Whole. From the structural identity, relating IS experiencing. Therefore, everything that exists experiences. This is not panpsychism as traditionally conceived—it's a mathematical consequence of relational ontology.

Proof files:

• Proposition_01_proven.v: Universal connectivity (∀x∈U_x, ∃y∈U_x: R'(x,y))
• Experience_Is_Relating.v: Relating = experiencing
• Consciousness_Structural_Framework.v: Theorem every_entity_has_experiential_structure

The question shifts from "which systems are conscious?" to "what is the structure of experiential richness for this system?"

Experience is not binary. It varies continuously in richness:

Minimal ←───────────────────────────────→ Maximal

A simple relation (particle interacting with field) has minimal experiential structure. A complex self-referential nested relational tensor (human brain) has rich experiential structure. Both experience—they differ in richness, not in having versus lacking experience.

Proof files:

• Thresholds_And_Metrics_Dissolved.v: Theorem richness_is_continuous_spectrum
• Consciousness_Structural_Framework.v: Theorem experiential_richness_continuous

What we call "consciousness" is experience above certain richness thresholds. These thresholds are definitional choices, not empirical discoveries. Like "tall" for height above a chosen value, "conscious" marks a region of the experiential spectrum we've decided to name.

Different contexts warrant different thresholds. The threshold for legal personhood differs from the threshold for moral consideration differs from the threshold for scientific study. All are valid for their purposes. None is the "correct" threshold.

Proof files:

• Thresholds_And_Metrics_Dissolved.v: Theorem thresholds_are_definitional
• Thresholds_And_Metrics_Dissolved.v: Theorem multiple_thresholds_valid
• Thresholds_And_Metrics_Dissolved.v: Theorem threshold_question_dissolution
• Consciousness_Structural_Framework.v: Theorem thresholds_are_choices

Relational Tensors encode multi-dimensional relationships between entities:

R^{β₁β₂...βₘ}_{α₁α₂...αₙ}(Eᵢ, Eⱼ, ...)

The upper indices denote relational attributes or states. The lower indices denote effects or outcomes. The number of indices represents relational complexity.

Since relating IS experiencing, these tensors directly encode experiential structure. A richer tensor configuration is not correlated with richer experience—it IS richer experience.

Proof files:

• Proposition_05_RelationalTensor_proven.v: RT definition and properties
• Proposition_04_RelationalSystem_proven.v: Relational system structure
• Experience_Is_Relating.v: Identity of relation and experience

NRTs extend RTs by embedding simpler RTs into higher-order structures:

Base Case (Direct Relations): NRT₁(Eᵢ, Eⱼ) = Rᵢ,ⱼ

Recursive Case (Indirect Relations): NRT₂(Eᵢ, Eⱼ) = Σₖ(Rᵢ,ₖ ⊗ Rₖ,ⱼ)

Further Recursion: NRT₃(Eᵢ, Eⱼ) = Σₖ(NRT₂(Eᵢ, Eₖ) ⊗ NRT₂(Eₖ, Eⱼ))

This recursive nesting captures increasingly complex relational—and therefore experiential—structures. Higher nesting levels correspond to richer experiential depth, including the recursive self-awareness characteristic of what we call consciousness.

Proof files:

• Prop_NestedRelationalTensors_proven.v: NRT construction and properties
• Proposition_27_HierarchicalNatureOfRelations_proven.v: Hierarchical structure
• NRT_Structure_Uniqueness.v: Uniqueness of NRT structure
• UCF_NRT_Scale_Predictions.v: Multi-scale NRT dynamics

The five metrics measure aspects of relational structure. Since relational structure IS experiential structure, they measure experiential richness directly—not by correlation but by identity.

Proof files for metric-experience identity:

• Thresholds_And_Metrics_Dissolved.v: Theorem all_metrics_are_relational
• Thresholds_And_Metrics_Dissolved.v: Theorem metrics_measure_experience_directly
• Thresholds_And_Metrics_Dissolved.v: Theorem correspondence_question_dissolution

What it measures: Relational diversity and density—the richness of the relational web.

Mathematical Form:RCI = Σᵢ,ⱼ type(Tᵢⱼ) × wᵢⱼ × Tᵢⱼ

where Tᵢⱼ represents relational strengths and wᵢⱼ weights relationship diversity.

Experiential interpretation: Higher RCI means richer experiential content—more to experience, more ways of experiencing. A human brain's RCI vastly exceeds a thermostat's, corresponding to vastly richer experience.

Proof files:

• Consciousness_Structural_Framework.v: Theorem rci_well_defined
• Proposition_04_RelationalSystem_proven.v: Relational system complexity
• Thresholds_And_Metrics_Dissolved.v: rci_measures_complexity

What it measures: The degree of self-reference within the NRT—feedback loops where the system relates to itself.

Mathematical Form:SRD = Σᵢ Σⱼ Tᵢⱼ · Tⱼᵢ

where Tᵢⱼ · Tⱼᵢ represents bidirectional feedback.

Experiential interpretation: Self-reference creates recursive experiential depth—experience of experience, awareness of awareness. This is what distinguishes rich conscious experience from simple sentience. The formal proof shows this recursion is structurally incomplete (Gödelian), explaining why consciousness cannot fully know itself.

Proof files:

• Consciousness_Structural_Framework.v: Theorem srd_well_defined
• Perspectival_Incompleteness.v: Gödelian self-reference limits
• Proposition_37_InfluenceOfPerspectiveOnRelations_proven.v: Self-referential perspective
• Thresholds_And_Metrics_Dissolved.v: srd_measures_self_depth

What it measures: Coherence across relational data—how unified the relational configuration is.

Mathematical Form:ARI = (1 / P×Q) Σₚ,ᵧ ρ(Tₚ, Tᵧ)

where ρ(Tₚ, Tᵧ) is the correlation between NRT layers.

Experiential interpretation: Higher ARI means more unified experience. Disparate relational states integrate into coherent awareness rather than fragmenting into disconnected processes. This corresponds to the phenomenal unity of conscious experience.

Proof files:

• Consciousness_Structural_Framework.v: Theorem ari_well_defined
• Integration_Is_Relational.v: Theorem richness_equals_integration
• Proposition_25_InterdependenceSystemCohesion_proven.v: System cohesion
• Thresholds_And_Metrics_Dissolved.v: ari_measures_adaptivity

What it measures: The system's capacity to selectively amplify certain relations—attention.

Mathematical Form:SRF = maxⱼ(∂Tᵢⱼ/∂t)

measuring how quickly relational strengths can change.

Experiential interpretation: Higher SRF means greater capacity for focused attention—the ability to foreground some experiential content while backgrounding others. This is attention as understood phenomenologically: selective enhancement of certain experiential streams.

Proof files:

• Consciousness_Structural_Framework.v: Theorem srf_well_defined
• Proposition_23_DynamicEquilibrium_proven.v: Dynamic stability
• Proposition_44_ContextAsModifyingFactor_proven.v: Selective context effects
• Thresholds_And_Metrics_Dissolved.v: srf_measures_feedback

What it measures: Stability of relational configuration over time.

Mathematical Form:RCC = Σᵢ,ⱼ ∫ₜ₀ᵗ¹ |∂Tᵢⱼ/∂t| dt

Experiential interpretation: Higher RCC means more continuous experience—a stable sense of self persisting through time rather than moment-to-moment discontinuity. This grounds personal identity and temporal consciousness.

Proof files:

• Consciousness_Structural_Framework.v: Theorem rcc_well_defined
• Proposition_28_TemporalEvolutionOfRelations_proven.v: Temporal evolution
• Proposition_33_TemporalEvolutionOfRS_proven.v: RS temporal evolution
• Thresholds_And_Metrics_Dissolved.v: rcc_measures_closure

From Proposition 37, there is no objective perspective—every view is from somewhere. Every relation has a source, a position from which the relating occurs. This position IS the perspective.

Proof files:

• Proposition_37_InfluenceOfPerspectiveOnRelations_proven.v: No objective perspective exists
• Proposition_13_PointOfRelation_proven.v: Point of Relation (POR) structure
• Proposition_10_Direction_proven.v: Directionality of relations

Since everything relates (Proposition 1), everything has a perspective. A photon interacting with an electron has a perspective—minimal, lacking self-reference, but structurally present. What varies is not whether perspective exists but how rich it is.

Proof files:

• Proposition_01_proven.v: Universal connectivity
• Consciousness_Structural_Framework.v: Theorem every_entity_has_experiential_structure
• Experience_Is_Relating.v: Relating = experiencing

What we typically call "a perspective" (in the full conscious sense) is a perspective with high values across the metrics: rich relational content (RCI), recursive self-reference (SRD), unified integration (ARI), selective focus capacity (SRF), and temporal continuity (RCC).

The coupling tensor Cαβ(T) = Σᵧ f(Tαᵧ, Tᵧβ) measures how different relational states connect. High cumulative coupling P = Σα,β Cαβ(T) indicates a unified experiential field—what we recognize as coherent conscious experience.

Proof files:

• UCF_Explicit_Embeddings.v: Coupling structures
• Proposition_25_InterdependenceSystemCohesion_proven.v: System cohesion
• Consciousness_Structural_Framework.v: coupling_well_defined

Experiential richness varies continuously. The formal proof establishes: for any two richness levels r₁ < r₂, there exist intermediate levels. No natural gaps in the spectrum.

Proof files:

• Thresholds_And_Metrics_Dissolved.v: Theorem no_gaps_in_spectrum
• Consciousness_Structural_Framework.v: Theorem experiential_richness_continuous

When we ask "is this system conscious?", we're asking whether its experiential richness exceeds some threshold we've chosen. The choice depends on context.

For ethical consideration, we might set thresholds based on capacity for suffering. For legal personhood, on capacity for autonomous decision-making. For scientific study, on measurability of the relevant metrics. Each threshold is valid for its purpose.

Proof files:

• Thresholds_And_Metrics_Dissolved.v: Theorem correct_threshold_is_contextual
• Thresholds_And_Metrics_Dissolved.v: Theorem multiple_valid_thresholds

The question "what is the threshold for consciousness?" assumed there was one correct answer to discover. There isn't. The question dissolves into "what threshold serves this purpose?" which has many valid answers.

Similarly, "do the metrics correspond to consciousness?" assumed metrics and consciousness were separate things requiring correlation. They aren't. The metrics measure relational structure; relational structure IS experiential structure. The question was malformed.

Proof files:

• Thresholds_And_Metrics_Dissolved.v: Theorem threshold_question_dissolved
• Thresholds_And_Metrics_Dissolved.v: Theorem correspondence_question_dissolved

The framework is mathematical. What remains empirical are questions about particular instantiations.

What is the actual NRT structure of a human brain? An octopus nervous system? A neural network? These require measurement and analysis, not mathematical proof.

Related proof files (providing measurement framework):

• QM_Chemistry_Sensory_Connection.v: Quantum-to-sensory chain
• Sensory_Modality_Abstraction.v: Sensory modality structure
• Vision_Relational_Derivation.v: Visual system relations

What specific relational configurations correspond to specific qualia in particular organisms? The framework establishes that qualia ARE configurations; which configurations produce which qualia in which systems is empirical.

Proof files:

• Qualia_Are_Relational_Structure.v: Qualia = structure (identity)
• Qualia_Are_Relational_Structure.v: Theorem same_structure_same_quale
• Qualia_Are_Relational_Structure.v: Theorem inverted_qualia_impossible

How do we measure RCI, SRD, ARI, SRF, RCC in practice for biological or artificial systems? This requires developing empirical methods, not just mathematical definitions.

Proof files (providing theoretical grounding):

• Consciousness_Structural_Framework.v: All metric definitions
• Integration_Is_Relational.v: Integration = coupling measurement
• Proposition_18_DistanceOfRelation_proven.v: Relational distance measures
• MetricCore.v: Core metric definitions

The metrics can be applied to neural systems through connectivity analysis. Functional MRI, EEG coherence, and structural connectivity data can be analyzed for RCI (connection diversity), SRD (recurrent loops), ARI (cross-region integration), SRF (attention-related dynamics), and RCC (temporal stability).

This doesn't tell us WHETHER brains are conscious—they are, like everything. It measures HOW RICH their experiential structure is and how it varies across conditions (sleep, anesthesia, disorders of consciousness).

Proof files (theoretical foundation):

• Proposition_12_SensoryMechanism_proven.v: Sensory mechanism structure
• QM_Chemistry_Sensory_Connection.v: Physical basis of perception
• Relational_Spectrum.v: Spectrum of relational configurations

For artificial systems, the question shifts from "is this AI conscious?" to "what is the experiential richness structure of this system?" The metrics can be computed directly from the system's architecture and dynamics.

This has implications for AI ethics: systems with richer experiential structure may warrant greater moral consideration, though where to draw lines remains a normative choice.

Proof files:

• Consciousness_Structural_Framework.v: System-independent framework
• Thresholds_And_Metrics_Dissolved.v: Threshold choices are normative

Cross-system comparison becomes meaningful: how does octopus experiential structure compare to mammalian? How does a large language model's relational configuration compare to biological neural networks? The metrics provide common vocabulary for such comparisons.

Proof files:

• Proposition_40_RelationalEquivalence_proven.v: Relational equivalence
• Proposition_38_TransitivityOfRelation_proven.v: Relational transitivity

Consciousness, in the UCF/GUTT framework, is not a mysterious property that some systems have and others lack. Experience IS what relating is. Everything that relates—which is everything—experiences. What varies is richness.

The mathematical machinery of Relational Tensors, Nested Relational Tensors, and the five metrics (RCI, SRD, ARI, SRF, RCC) measures this richness. These are not proxies for consciousness that might or might not correlate with it. They measure relational structure directly, and relational structure IS experiential structure.

"Consciousness" is our label for rich experience—experience above thresholds we choose for particular purposes. The thresholds are definitional, not empirical. The spectrum is continuous.

What remains empirical are questions about particular systems: what structures do they have? 

How do we measure those structures? What specific mappings exist in specific organisms? These are questions about instantiations, not about the framework.

The formal proofs establish the mathematical structure. Whether this structure corresponds to physical reality is empirical. But the framework makes specific predictions, recovers established physics, and dissolves traditional problems. It stands as a coherent, testable account of consciousness as relational structure.

Experience_Is_Relating.v

• experience_relation_isomorphism: R(source,target) ≅ Experience(subject,content)
• experience_relation_round_trip: Bijection preservation
• hard_problem_dissolved: Category error established
• relation_has_subject_position: Source = subject
• relation_has_content: Target = content

Qualia_Are_Relational_Structure.v

• quale_is_configuration: Qualia = relational configurations
• same_structure_same_quale: Identical structure → identical quale
• different_structure_different_quale: Different structure → different quale
• inverted_qualia_impossible: Inverted qualia contradiction
• qualia_question_dissolved: "Why this quale?" = tautology

Integration_Is_Relational.v

• integration_defined_by_relations: Integration from NRT
• integration_always_nonneg: Non-negative
• richness_equals_integration: Experiential richness = integration
• sufficiency_question_dissolved: "Sufficient?" = tautology

Thresholds_And_Metrics_Dissolved.v

• richness_is_continuous_spectrum: No gaps
• thresholds_are_definitional: Context-dependent
• multiple_valid_thresholds: Multiple thresholds coexist
• threshold_question_dissolved: Question dissolves
• all_metrics_are_relational: Metrics measure relations
• correspondence_question_dissolved: Direct measurement
• metrics_measure_experience_directly: By identity, not correlation

Consciousness_Structural_Framework.v

• every_entity_has_experiential_structure: Universal experience
• experiential_richness_continuous: Continuous spectrum
• self_reference_increases_richness: Self-ref → richer
• perspectives_structurally_incomplete: Gödelian limits
• below_threshold_has_experience: Below threshold still experiences
• thresholds_are_choices: Multiple valid thresholds

Proposition_01_proven.v — Universal connectivity Proposition_04_RelationalSystem_proven.v — RS structure Proposition_05_RelationalTensor_proven.v — RT definition Proposition_10_Direction_proven.v — Directionality Proposition_12_SensoryMechanism_proven.v — Sensory mechanism Proposition_13_PointOfRelation_proven.v — Point of relation Proposition_22_EmergenceOfNovelRelations_proven.v — Emergence Proposition_23_DynamicEquilibrium_proven.v — Dynamic equilibrium Proposition_25_InterdependenceSystemCohesion_proven.v — System cohesion Proposition_27_HierarchicalNatureOfRelations_proven.v — Hierarchy Proposition_28_TemporalEvolutionOfRelations_proven.v — Temporal evolution Proposition_33_TemporalEvolutionOfRS_proven.v — RS evolution Proposition_37_InfluenceOfPerspectiveOnRelations_proven.v — No objective view Proposition_44_ContextAsModifyingFactor_proven.v — Context effects

Prop_NestedRelationalTensors_proven.v — NRT construction NRT_Structure_Uniqueness.v — NRT uniqueness UCF_NRT_Scale_Predictions.v — Multi-scale dynamics Perspectival_Incompleteness.v — Gödelian self-reference limits QM_Chemistry_Sensory_Connection.v — Perception chain Sensory_Modality_Abstraction.v — Modality structure Vision_Relational_Derivation.v — Visual system Relational_Spectrum.v — Spectrum configurations MetricCore.v — Core metrics UCF_Explicit_Embeddings.v — Coupling structures

UCF_Recovery_Theorems.v — QM and GR recovery UCF_Recovery_Theorems_ZeroAxiom.v — Zero-axiom recovery UCF_Subsumes_Schrodinger_proven.v — Schrödinger subsumption UCF_Subsumes_Einstein_Field_Equations_Proven.v — Einstein subsumption Maxwell_Recovery.v — Maxwell recovery UCF_Unifies_QM_GR.v — QM-GR unification

All source code, proofs, and comprehensive documentation are freely available at github.com/relationalexistence/UCF-GUTT. This represents not speculative philosophy but rigorous, machine-verified foundations for understanding reality as fundamentally relational.

© 2023–2025 Michael Fillippini. All Rights Reserved. UCF/GUTT™ Research & Evaluation License v1.1