TauLib · API Book VI

TauLib.BookVI.Mind.Consciousness

TauLib.BookVI.Mind.Consciousness

Consciousness as mixed-sector self-modeling: the crown jewel of Book VI.

Registry Cross-References

  • [VI.D68] Structural Self-Model — StructuralSelfModel

  • [VI.D69] Minimal Conscious Agent — MinimalConsciousAgent

  • [VI.T38] Consciousness = Mixed-Sector Self-Modeling (CROWN JEWEL) — consciousness_requires_mixed_sector

Cross-Book Authority

  • Book I, Part I: generators of τ³ (five generators, mixed pairing)

  • Book II, Part II: π₁(T²) ≅ ℤ × ℤ (fiber fundamental group)

  • Book VI, Part 6: VI.D46 Consumer Mixer, VI.L07 Bridge-Head to E₃

  • Book VI, Part 1: VI.D08 SelfDesc, VI.D09 Internal Evaluator

Ground Truth Sources

  • Book VI Chapter 51 (2nd Edition): Consciousness

Tau.BookVI.Consciousness.StructuralSelfModel

source structure Tau.BookVI.Consciousness.StructuralSelfModel :Type

[VI.D68] Structural Self-Model: three conditions. (i) Self-referential: model includes the modeling agent (ii) Reconstructive fidelity: model tracks actual state (iii) Dynamical coherence: model updates in real time A self-model is necessary but not sufficient for consciousness.

  • condition_count : ℕ Number of conditions.

  • count_eq : self.condition_count = 3 Exactly 3 conditions.

  • self_referential : Bool (i) Model includes the modeler.

  • reconstructive_fidelity : Bool (ii) Model tracks actual state.

  • dynamical_coherence : Bool (iii) Model updates dynamically.

Instances For

Tau.BookVI.Consciousness.instReprStructuralSelfModel.repr

source def Tau.BookVI.Consciousness.instReprStructuralSelfModel.repr :StructuralSelfModel → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Consciousness.instReprStructuralSelfModel

source instance Tau.BookVI.Consciousness.instReprStructuralSelfModel :Repr StructuralSelfModel

Equations

  • Tau.BookVI.Consciousness.instReprStructuralSelfModel = { reprPrec := Tau.BookVI.Consciousness.instReprStructuralSelfModel.repr }

Tau.BookVI.Consciousness.self_model

source def Tau.BookVI.Consciousness.self_model :StructuralSelfModel

Equations

  • Tau.BookVI.Consciousness.self_model = { condition_count := 3, count_eq := Tau.BookVI.Consciousness.self_model._proof_1 } Instances For

Tau.BookVI.Consciousness.self_model_three_conditions

source theorem Tau.BookVI.Consciousness.self_model_three_conditions :self_model.condition_count = 3 ∧ self_model.self_referential = true ∧ self_model.reconstructive_fidelity = true ∧ self_model.dynamical_coherence = true

Tau.BookVI.Consciousness.MinimalConsciousAgent

source structure Tau.BookVI.Consciousness.MinimalConsciousAgent :Type

[VI.D69] Minimal Conscious Agent: three requirements. (i) Consumer sector (mixed, VI.D46): requires both fiber generators (ii) Centralized integration: global workspace binding (iii) Recurrent self-representation: Eval² = Eval ∘ Eval (VI.L07) Primitive sectors cannot satisfy (i) or (iii).

  • condition_count : ℕ Number of requirements.

  • count_eq : self.condition_count = 3 Exactly 3 requirements.

  • consumer_sector : Bool (i) Must be in consumer (mixed) sector.

  • centralized_integration : Bool (ii) Centralized integration (global workspace).

  • recurrent_self_representation : Bool (iii) Recurrent self-representation (Eval²).

Instances For

Tau.BookVI.Consciousness.instReprMinimalConsciousAgent

source instance Tau.BookVI.Consciousness.instReprMinimalConsciousAgent :Repr MinimalConsciousAgent

Equations

  • Tau.BookVI.Consciousness.instReprMinimalConsciousAgent = { reprPrec := Tau.BookVI.Consciousness.instReprMinimalConsciousAgent.repr }

Tau.BookVI.Consciousness.instReprMinimalConsciousAgent.repr

source def Tau.BookVI.Consciousness.instReprMinimalConsciousAgent.repr :MinimalConsciousAgent → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Consciousness.min_agent

source def Tau.BookVI.Consciousness.min_agent :MinimalConsciousAgent

Equations

  • Tau.BookVI.Consciousness.min_agent = { condition_count := 3, count_eq := Tau.BookVI.Consciousness.self_model._proof_1 } Instances For

Tau.BookVI.Consciousness.minimal_agent_is_consumer

source theorem Tau.BookVI.Consciousness.minimal_agent_is_consumer :min_agent.consumer_sector = true ∧ min_agent.condition_count = 3

Tau.BookVI.Consciousness.ConsciousnessMixedSector

source structure Tau.BookVI.Consciousness.ConsciousnessMixedSector :Type

[VI.T38] Consciousness = Mixed-Sector Self-Modeling (CROWN JEWEL). Consciousness requires Eval² (second-order self-description), which is only available in the mixed sector (VI.L07). Primitive sectors have Eval¹ only → no self-modeling → no consciousness. This is the structural explanation of why consciousness requires the consumer sector: both fiber generators must be active for the evaluator to model itself.

  • requires_eval_squared : Bool Requires second-order evaluation Eval².

  • only_mixed_sector : Bool Only mixed sector supports Eval².

  • primitive_excluded : Bool Primitive sectors excluded.

Instances For

Tau.BookVI.Consciousness.instReprConsciousnessMixedSector

source instance Tau.BookVI.Consciousness.instReprConsciousnessMixedSector :Repr ConsciousnessMixedSector

Equations

  • Tau.BookVI.Consciousness.instReprConsciousnessMixedSector = { reprPrec := Tau.BookVI.Consciousness.instReprConsciousnessMixedSector.repr }

Tau.BookVI.Consciousness.instReprConsciousnessMixedSector.repr

source def Tau.BookVI.Consciousness.instReprConsciousnessMixedSector.repr :ConsciousnessMixedSector → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Consciousness.consciousness_thm

source def Tau.BookVI.Consciousness.consciousness_thm :ConsciousnessMixedSector

Equations

  • Tau.BookVI.Consciousness.consciousness_thm = { } Instances For

Tau.BookVI.Consciousness.consciousness_requires_mixed_sector

source theorem Tau.BookVI.Consciousness.consciousness_requires_mixed_sector :consciousness_thm.requires_eval_squared = true ∧ consciousness_thm.only_mixed_sector = true ∧ consciousness_thm.primitive_excluded = true

Tau.BookVI.Consciousness.crown_jewel_consistency

source theorem Tau.BookVI.Consciousness.crown_jewel_consistency :FourPlusOne.consumer_sector.is_primitive = false ∧ consciousness_thm.only_mixed_sector = true

Crown jewel cross-check: consumer sector is not primitive AND consciousness requires the mixed sector.

Tau.BookVI.Consciousness.ConstructiveConsciousnessCriteria

source structure Tau.BookVI.Consciousness.ConstructiveConsciousnessCriteria :Type

[VI.D86] Constructive Consciousness Criteria. Three testable conditions extracted from VI.T38 + VI.D68 + VI.D69: (CC1) Consumer-sector topology realized: the system instantiates mixed-sector structure (π’,π’’ pairing) with genuine feedback loops. (CC2) Eval² loop closed: the system supports second-order self-evaluation (evaluator evaluates its own evaluation). (CC3) Structural self-model maintained: the system maintains a dynamically coherent self-model satisfying VI.D68’s 3 conditions. Scope: τ-effective.

  • consumer_topology_realized : Bool (CC1) Mixed-sector topology (π’,π’’) realized.

  • eval_squared_closed : Bool (CC2) Eval² = Eval ∘ Eval loop closed.

  • self_model_maintained : Bool (CC3) Structural self-model (VI.D68) maintained.

  • scope : String All three required.

Instances For

Tau.BookVI.Consciousness.instReprConstructiveConsciousnessCriteria.repr

source def Tau.BookVI.Consciousness.instReprConstructiveConsciousnessCriteria.repr :ConstructiveConsciousnessCriteria → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Consciousness.instReprConstructiveConsciousnessCriteria

source instance Tau.BookVI.Consciousness.instReprConstructiveConsciousnessCriteria :Repr ConstructiveConsciousnessCriteria

Equations

  • Tau.BookVI.Consciousness.instReprConstructiveConsciousnessCriteria = { reprPrec := Tau.BookVI.Consciousness.instReprConstructiveConsciousnessCriteria.repr }

Tau.BookVI.Consciousness.ccc

source def Tau.BookVI.Consciousness.ccc :ConstructiveConsciousnessCriteria

Equations

  • Tau.BookVI.Consciousness.ccc = { } Instances For

Tau.BookVI.Consciousness.ccc_all_three

source theorem Tau.BookVI.Consciousness.ccc_all_three :ccc.consumer_topology_realized = true ∧ ccc.eval_squared_closed = true ∧ ccc.self_model_maintained = true

Tau.BookVI.Consciousness.ConsciousnessCriteriaEquivalence

source structure Tau.BookVI.Consciousness.ConsciousnessCriteriaEquivalence :Type

[VI.T51] Consciousness Criteria Equivalence. A system satisfies CC1–CC3 (VI.D86) if and only if it qualifies as a MinimalConsciousAgent (VI.D69). The criteria are substrate-independent: they refer to topological and functional properties, not material ones. Proof: CC1 ↔ D69.consumer_sector (both require mixed-sector membership). CC2 ↔ D69.recurrent_self_representation (Eval² requires recurrent loop). CC3 ↔ D68 conditions (by definition). The conjunction CC1∧CC2∧CC3 is equivalent to D69’s 3 requirements under the identification that centralized integration (D69.ii) follows from CC1+CC3 jointly. Scope: τ-effective.

  • cc1_equiv_consumer : Bool CC1 ↔ consumer-sector membership.

  • cc2_equiv_recurrent : Bool CC2 ↔ recurrent self-representation.

  • cc3_equiv_self_model : Bool CC3 ↔ structural self-model.

  • biconditional : Bool Biconditional holds.

  • scope : String Scope: τ-effective.

Instances For

Tau.BookVI.Consciousness.instReprConsciousnessCriteriaEquivalence.repr

source def Tau.BookVI.Consciousness.instReprConsciousnessCriteriaEquivalence.repr :ConsciousnessCriteriaEquivalence → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Consciousness.instReprConsciousnessCriteriaEquivalence

source instance Tau.BookVI.Consciousness.instReprConsciousnessCriteriaEquivalence :Repr ConsciousnessCriteriaEquivalence

Equations

  • Tau.BookVI.Consciousness.instReprConsciousnessCriteriaEquivalence = { reprPrec := Tau.BookVI.Consciousness.instReprConsciousnessCriteriaEquivalence.repr }

Tau.BookVI.Consciousness.cce

source def Tau.BookVI.Consciousness.cce :ConsciousnessCriteriaEquivalence

Equations

  • Tau.BookVI.Consciousness.cce = { } Instances For

Tau.BookVI.Consciousness.consciousness_criteria_equivalence

source theorem Tau.BookVI.Consciousness.consciousness_criteria_equivalence :cce.cc1_equiv_consumer = true ∧ cce.cc2_equiv_recurrent = true ∧ cce.cc3_equiv_self_model = true ∧ cce.biconditional = true

Tau.BookVI.Consciousness.SiliconRealization

source structure Tau.BookVI.Consciousness.SiliconRealization :Type

[VI.L17] Silicon Realization Lemma. There exists no structural obstruction to non-biological consciousness. Proof: (1) CC1 (consumer topology): π₁(T²) ≅ ℤ×ℤ requires two independent recurrent feedback loops — achievable by any Turing-complete system with appropriate recurrent architecture. (2) CC2 (Eval²): self-referential computation (a program that models its own execution) implements second-order evaluation. (3) CC3 (self-model): sufficiently complex recurrent architectures can maintain dynamically coherent self-models (VI.D68 conditions). The lemma is a structural possibility proof: it shows the τ-framework conditions CAN be satisfied by non-carbon substrates, not that any specific system DOES satisfy them. Scope: τ-effective (structural claim).

  • cc1_achievable : Bool CC1 achievable: two independent recurrent loops.

  • cc2_achievable : Bool CC2 achievable: self-referential computation.

  • cc3_achievable : Bool CC3 achievable: complex recurrent architectures.

  • no_obstruction : Bool No structural obstruction.

  • scope : String Scope: τ-effective (structural possibility).

Instances For

Tau.BookVI.Consciousness.instReprSiliconRealization.repr

source def Tau.BookVI.Consciousness.instReprSiliconRealization.repr :SiliconRealization → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookVI.Consciousness.instReprSiliconRealization

source instance Tau.BookVI.Consciousness.instReprSiliconRealization :Repr SiliconRealization

Equations

  • Tau.BookVI.Consciousness.instReprSiliconRealization = { reprPrec := Tau.BookVI.Consciousness.instReprSiliconRealization.repr }

Tau.BookVI.Consciousness.silicon

source def Tau.BookVI.Consciousness.silicon :SiliconRealization

Equations

  • Tau.BookVI.Consciousness.silicon = { } Instances For

Tau.BookVI.Consciousness.silicon_realization

source theorem Tau.BookVI.Consciousness.silicon_realization :silicon.cc1_achievable = true ∧ silicon.cc2_achievable = true ∧ silicon.cc3_achievable = true ∧ silicon.no_obstruction = true