TauLib · API Book VI

TauLib.BookVI.Source.SourceSector

TauLib.BookVI.Source.SourceSector

Source sector (Part 4): π’-sector structure generation on fiber. Archetype: Plants. Dominant forces: Hodge + BSD.

Registry Cross-References

  • [VI.D36] Source Sector — SourceSectorDef

  • [VI.D37] Structure Generation Predicate — StructureGenerationPredicate

  • [VI.T20] Source = π’-Fiber Production — source_is_pi_prime_production

  • [VI.D38] Carbon Fixation as Canonical Production — CarbonFixation

  • [VI.P13] Quantum Coherence in FMO Complex — fmo_quantum_coherence

Cross-Book Authority

  • Book I, Part I: π’ generator (solenoidal, fiber T²)

  • Book II, Part II: τ³ = τ¹ ×_f T² fibration structure

  • Book III, Part IV: Hodge force (harmonic decomposition, morphogenesis)

  • Book III, Part V: BSD force (rational points, genetic code)

  • Book III, Part I: P vs NP force (quantum coherence)

Ground Truth Sources

  • Book VI Chapter 23 (2nd Edition): The Source Sector

  • Book VI Chapter 24 (2nd Edition): Photosynthesis

Tau.BookVI.Source.SourceSectorDef

source structure Tau.BookVI.Source.SourceSectorDef :Type

[VI.D36] Source Sector: π’-sector on fiber T². Life Loop restricted to structure generation on the fiber. Generator: π’ (solenoidal, Book I Part I). Dominant forces: Hodge + BSD (Book III, Parts IV–V).

  • generator : String Generator is pi’ (fiber).

  • is_primitive : Bool Sector is primitive (single generator).

  • archetype : String Archetype organism.

  • dominant_hodge : Bool Dominant force 1: Hodge (harmonic decomposition → morphogenesis).

  • dominant_bsd : Bool Dominant force 2: BSD (rank of rational points → genetic code).

Instances For

Tau.BookVI.Source.instReprSourceSectorDef

source instance Tau.BookVI.Source.instReprSourceSectorDef :Repr SourceSectorDef

Equations

  • Tau.BookVI.Source.instReprSourceSectorDef = { reprPrec := Tau.BookVI.Source.instReprSourceSectorDef.repr }

Tau.BookVI.Source.instReprSourceSectorDef.repr

source def Tau.BookVI.Source.instReprSourceSectorDef.repr :SourceSectorDef → ℕ → Std.Format

Equations

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

Tau.BookVI.Source.source_def

source def Tau.BookVI.Source.source_def :SourceSectorDef

Equations

  • Tau.BookVI.Source.source_def = { } Instances For

Tau.BookVI.Source.source_generator_match

source theorem Tau.BookVI.Source.source_generator_match :source_def.generator = FourPlusOne.source_sector.generator

Source sector matches the FourPlusOne source_sector definition.

Tau.BookVI.Source.StructureGenerationPredicate

source structure Tau.BookVI.Source.StructureGenerationPredicate :Type

[VI.D37] Structure Generation Predicate: 3 conditions. (i) Net production of structural complexity on T² fiber (ii) Hodge capacity gradient positive (Book III, Part IV) (iii) Energy input from base τ¹ (photon capture or equivalent)

  • condition_count : ℕ Number of conditions.

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

  • net_production : Bool (i) Net production on fiber.

  • hodge_gradient_positive : Bool (ii) Hodge capacity gradient positive.

  • base_energy_input : Bool (iii) Energy input from base.

Instances For

Tau.BookVI.Source.instReprStructureGenerationPredicate.repr

source def Tau.BookVI.Source.instReprStructureGenerationPredicate.repr :StructureGenerationPredicate → ℕ → Std.Format

Equations

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

Tau.BookVI.Source.instReprStructureGenerationPredicate

source instance Tau.BookVI.Source.instReprStructureGenerationPredicate :Repr StructureGenerationPredicate

Equations

  • Tau.BookVI.Source.instReprStructureGenerationPredicate = { reprPrec := Tau.BookVI.Source.instReprStructureGenerationPredicate.repr }

Tau.BookVI.Source.struct_gen

source def Tau.BookVI.Source.struct_gen :StructureGenerationPredicate

Equations

  • Tau.BookVI.Source.struct_gen = { condition_count := 3, count_eq := Tau.BookVI.Source.struct_gen._proof_1 } Instances For

Tau.BookVI.Source.generation_three_conditions

source theorem Tau.BookVI.Source.generation_three_conditions :struct_gen.condition_count = 3

Tau.BookVI.Source.generation_all_hold

source theorem Tau.BookVI.Source.generation_all_hold :struct_gen.net_production = true ∧ struct_gen.hodge_gradient_positive = true ∧ struct_gen.base_energy_input = true

Tau.BookVI.Source.SourceProduction

source structure Tau.BookVI.Source.SourceProduction :Type

[VI.T20] Source = π’-Fiber Production Theorem. A source Life loop has nontrivial π’-winding on the fiber with net positive structure generation.

  • winding_pi_prime : ℕ Winding on π’ (fiber).

  • pi_prime_nontrivial : self.winding_pi_prime ≥ 1 Winding is nontrivial (≥ 1).

  • net_generation : Bool Net structure generation.

Instances For

Tau.BookVI.Source.instReprSourceProduction

source instance Tau.BookVI.Source.instReprSourceProduction :Repr SourceProduction

Equations

  • Tau.BookVI.Source.instReprSourceProduction = { reprPrec := Tau.BookVI.Source.instReprSourceProduction.repr }

Tau.BookVI.Source.instReprSourceProduction.repr

source def Tau.BookVI.Source.instReprSourceProduction.repr :SourceProduction → ℕ → Std.Format

Equations

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

Tau.BookVI.Source.source_prod

source def Tau.BookVI.Source.source_prod :SourceProduction

Equations

  • Tau.BookVI.Source.source_prod = { winding_pi_prime := 1, pi_prime_nontrivial := Tau.BookVI.Source.source_prod._proof_1 } Instances For

Tau.BookVI.Source.source_is_pi_prime_production

source theorem Tau.BookVI.Source.source_is_pi_prime_production :source_prod.winding_pi_prime ≥ 1 ∧ source_prod.net_generation = true

Tau.BookVI.Source.CarbonFixation

source structure Tau.BookVI.Source.CarbonFixation :Type

[VI.D38] Carbon Fixation as Canonical Source Production. Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. The archetypal structure generation process.

  • co2_per_glucose : ℕ CO₂ molecules fixed per glucose.

  • co2_eq : self.co2_per_glucose = 6 Exactly 6.

  • hodge_driven : Bool Driven by Hodge capacity gradient.

  • global_fixation_gt : ℕ Global rate: ~120 Gt C/yr.

Instances For

Tau.BookVI.Source.instReprCarbonFixation

source instance Tau.BookVI.Source.instReprCarbonFixation :Repr CarbonFixation

Equations

  • Tau.BookVI.Source.instReprCarbonFixation = { reprPrec := Tau.BookVI.Source.instReprCarbonFixation.repr }

Tau.BookVI.Source.instReprCarbonFixation.repr

source def Tau.BookVI.Source.instReprCarbonFixation.repr :CarbonFixation → ℕ → Std.Format

Equations

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

Tau.BookVI.Source.carbon_fix

source def Tau.BookVI.Source.carbon_fix :CarbonFixation

Equations

  • Tau.BookVI.Source.carbon_fix = { co2_per_glucose := 6, co2_eq := Tau.BookVI.Source.carbon_fix._proof_1 } Instances For

Tau.BookVI.Source.FMOCoherence

source structure Tau.BookVI.Source.FMOCoherence :Type

[VI.P13] Quantum Coherence in FMO Complex (conjectural). The Fenna-Matthews-Olson complex exploits quantum coherence for near-unity energy transfer efficiency. Interpreted as P vs NP force at E₂ (Book III, Part I): the complex solves an NP-hard optimization (exciton routing) in polynomial time by exploiting quantum superposition.

  • efficiency_percent : ℕ Transfer efficiency (percent).

  • high_efficiency : self.efficiency_percent ≥ 95 Near-unity: ≥ 95%.

  • p_vs_np_connection : Bool Connected to P vs NP force (Book III, Part I).

  • scope : String Scope: conjectural.

Instances For

Tau.BookVI.Source.instReprFMOCoherence

source instance Tau.BookVI.Source.instReprFMOCoherence :Repr FMOCoherence

Equations

  • Tau.BookVI.Source.instReprFMOCoherence = { reprPrec := Tau.BookVI.Source.instReprFMOCoherence.repr }

Tau.BookVI.Source.instReprFMOCoherence.repr

source def Tau.BookVI.Source.instReprFMOCoherence.repr :FMOCoherence → ℕ → Std.Format

Equations

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

Tau.BookVI.Source.fmo

source def Tau.BookVI.Source.fmo :FMOCoherence

Equations

  • Tau.BookVI.Source.fmo = { efficiency_percent := 99, high_efficiency := Tau.BookVI.Source.fmo._proof_2 } Instances For

Tau.BookVI.Source.fmo_quantum_coherence

source theorem Tau.BookVI.Source.fmo_quantum_coherence :fmo.efficiency_percent ≥ 95 ∧ fmo.p_vs_np_connection = true