TauLib · API Book VI

TauLib.BookVI.Sectors.LifeLoop

TauLib.BookVI.Sectors.LifeLoop

Life Loop class: triple (D, γ, h) — distinction + metabolic cycle + homotopy class. DecodeTarget, DecodeHorizon, Metabolic Fiber Theorem, Consumer Mixer Uniqueness.

Registry Cross-References

  • [VI.D10] Life Loop Class — LifeLoopClass

  • [VI.D11] DecodeTarget — DecodeTarget

  • [VI.D12] DecodeHorizon — DecodeHorizon

  • [VI.D13] Source Sub-Class — SourceSubClass

  • [VI.D14] Closure Sub-Class — ClosureSubClass

  • [VI.T05] Metabolic Fiber Theorem — metabolic_fiber_theorem

  • [VI.T06] Consumer Mixer Uniqueness — consumer_mixer_uniqueness

  • [VI.P06] Seven Forces at E₂ — seven_forces_e2

  • [VI.P07] Force-Sector Matching — force_sector_matching

Ground Truth Sources

  • Book VI Chapter 7 (2nd Edition): Life Loop Class

Tau.BookVI.LifeLoop.LifeLoopClass

source structure Tau.BookVI.LifeLoop.LifeLoopClass :Type

[VI.D10] Life Loop class: triple (D, γ, h).

  • component_count : ℕ
  • count_eq : self.component_count = 3 Instances For

Tau.BookVI.LifeLoop.instReprLifeLoopClass

source instance Tau.BookVI.LifeLoop.instReprLifeLoopClass :Repr LifeLoopClass

Equations

  • Tau.BookVI.LifeLoop.instReprLifeLoopClass = { reprPrec := Tau.BookVI.LifeLoop.instReprLifeLoopClass.repr }

Tau.BookVI.LifeLoop.instReprLifeLoopClass.repr

source def Tau.BookVI.LifeLoop.instReprLifeLoopClass.repr :LifeLoopClass → ℕ → Std.Format

Equations

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

Tau.BookVI.LifeLoop.life_loop

source def Tau.BookVI.LifeLoop.life_loop :LifeLoopClass

Equations

  • Tau.BookVI.LifeLoop.life_loop = { component_count := 3, count_eq := Tau.BookVI.LifeLoop.life_loop._proof_1 } Instances For

Tau.BookVI.LifeLoop.DecodeTarget

source structure Tau.BookVI.LifeLoop.DecodeTarget :Type

[VI.D11] DecodeTarget: selects minimal-defect element of blueprint ball.

  • selects_minimum : Bool
  • unique_minimizer : Bool Instances For

Tau.BookVI.LifeLoop.instReprDecodeTarget

source instance Tau.BookVI.LifeLoop.instReprDecodeTarget :Repr DecodeTarget

Equations

  • Tau.BookVI.LifeLoop.instReprDecodeTarget = { reprPrec := Tau.BookVI.LifeLoop.instReprDecodeTarget.repr }

Tau.BookVI.LifeLoop.instReprDecodeTarget.repr

source def Tau.BookVI.LifeLoop.instReprDecodeTarget.repr :DecodeTarget → ℕ → Std.Format

Equations

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

Tau.BookVI.LifeLoop.decode_target

source def Tau.BookVI.LifeLoop.decode_target :DecodeTarget

Equations

  • Tau.BookVI.LifeLoop.decode_target = { } Instances For

Tau.BookVI.LifeLoop.DecodeHorizon

source structure Tau.BookVI.LifeLoop.DecodeHorizon :Type

[VI.D12] DecodeHorizon: extracts unique ω-germ code constant across B_n.

  • extracts_code : Bool
  • code_constant : Bool Instances For

Tau.BookVI.LifeLoop.instReprDecodeHorizon

source instance Tau.BookVI.LifeLoop.instReprDecodeHorizon :Repr DecodeHorizon

Equations

  • Tau.BookVI.LifeLoop.instReprDecodeHorizon = { reprPrec := Tau.BookVI.LifeLoop.instReprDecodeHorizon.repr }

Tau.BookVI.LifeLoop.instReprDecodeHorizon.repr

source def Tau.BookVI.LifeLoop.instReprDecodeHorizon.repr :DecodeHorizon → ℕ → Std.Format

Equations

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

Tau.BookVI.LifeLoop.decode_horizon

source def Tau.BookVI.LifeLoop.decode_horizon :DecodeHorizon

Equations

  • Tau.BookVI.LifeLoop.decode_horizon = { } Instances For

Tau.BookVI.LifeLoop.SourceSubClass

source structure Tau.BookVI.LifeLoop.SourceSubClass :Type

[VI.D13] Source sub-class: loops with dominant π’-winding.

  • generator : String
  • archetype : String Instances For

Tau.BookVI.LifeLoop.instReprSourceSubClass.repr

source def Tau.BookVI.LifeLoop.instReprSourceSubClass.repr :SourceSubClass → ℕ → Std.Format

Equations

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

Tau.BookVI.LifeLoop.instReprSourceSubClass

source instance Tau.BookVI.LifeLoop.instReprSourceSubClass :Repr SourceSubClass

Equations

  • Tau.BookVI.LifeLoop.instReprSourceSubClass = { reprPrec := Tau.BookVI.LifeLoop.instReprSourceSubClass.repr }

Tau.BookVI.LifeLoop.ClosureSubClass

source structure Tau.BookVI.LifeLoop.ClosureSubClass :Type

[VI.D14] Closure sub-class: loops with dominant π’‘-winding.

  • generator : String
  • archetype : String Instances For

Tau.BookVI.LifeLoop.instReprClosureSubClass.repr

source def Tau.BookVI.LifeLoop.instReprClosureSubClass.repr :ClosureSubClass → ℕ → Std.Format

Equations

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

Tau.BookVI.LifeLoop.instReprClosureSubClass

source instance Tau.BookVI.LifeLoop.instReprClosureSubClass :Repr ClosureSubClass

Equations

  • Tau.BookVI.LifeLoop.instReprClosureSubClass = { reprPrec := Tau.BookVI.LifeLoop.instReprClosureSubClass.repr }

Tau.BookVI.LifeLoop.MetabolicFiberTheorem

source structure Tau.BookVI.LifeLoop.MetabolicFiberTheorem :Type

[VI.T05] Metabolic Fiber Theorem: every Life loop factors through Loop_src × Loop_rec × Loop_base.

  • factor_count : ℕ
  • count_eq : self.factor_count = 3
  • src_nontrivial : Bool
  • rec_nontrivial : Bool Instances For

Tau.BookVI.LifeLoop.instReprMetabolicFiberTheorem

source instance Tau.BookVI.LifeLoop.instReprMetabolicFiberTheorem :Repr MetabolicFiberTheorem

Equations

  • Tau.BookVI.LifeLoop.instReprMetabolicFiberTheorem = { reprPrec := Tau.BookVI.LifeLoop.instReprMetabolicFiberTheorem.repr }

Tau.BookVI.LifeLoop.instReprMetabolicFiberTheorem.repr

source def Tau.BookVI.LifeLoop.instReprMetabolicFiberTheorem.repr :MetabolicFiberTheorem → ℕ → Std.Format

Equations

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

Tau.BookVI.LifeLoop.metabolic_fiber

source def Tau.BookVI.LifeLoop.metabolic_fiber :MetabolicFiberTheorem

Equations

  • Tau.BookVI.LifeLoop.metabolic_fiber = { factor_count := 3, count_eq := Tau.BookVI.LifeLoop.life_loop._proof_1 } Instances For

Tau.BookVI.LifeLoop.metabolic_fiber_theorem

source theorem Tau.BookVI.LifeLoop.metabolic_fiber_theorem :metabolic_fiber.factor_count = 3 ∧ metabolic_fiber.src_nontrivial = true ∧ metabolic_fiber.rec_nontrivial = true

Tau.BookVI.LifeLoop.ConsumerMixerUniqueness

source structure Tau.BookVI.LifeLoop.ConsumerMixerUniqueness :Type

[VI.T06] Consumer Mixer Uniqueness: exactly 1 admissible mixer on fiber pair.

  • mixer_count : ℕ
  • unique : self.mixer_count = 1
  • fiber_pair : Bool Instances For

Tau.BookVI.LifeLoop.instReprConsumerMixerUniqueness

source instance Tau.BookVI.LifeLoop.instReprConsumerMixerUniqueness :Repr ConsumerMixerUniqueness

Equations

  • Tau.BookVI.LifeLoop.instReprConsumerMixerUniqueness = { reprPrec := Tau.BookVI.LifeLoop.instReprConsumerMixerUniqueness.repr }

Tau.BookVI.LifeLoop.instReprConsumerMixerUniqueness.repr

source def Tau.BookVI.LifeLoop.instReprConsumerMixerUniqueness.repr :ConsumerMixerUniqueness → ℕ → Std.Format

Equations

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

Tau.BookVI.LifeLoop.consumer_mixer

source def Tau.BookVI.LifeLoop.consumer_mixer :ConsumerMixerUniqueness

Equations

  • Tau.BookVI.LifeLoop.consumer_mixer = { mixer_count := 1, unique := Tau.BookVI.LifeLoop.consumer_mixer._proof_1 } Instances For

Tau.BookVI.LifeLoop.consumer_mixer_uniqueness

source theorem Tau.BookVI.LifeLoop.consumer_mixer_uniqueness :consumer_mixer.mixer_count = 1 ∧ consumer_mixer.fiber_pair = true

Tau.BookVI.LifeLoop.seven_forces_e2

source theorem Tau.BookVI.LifeLoop.seven_forces_e2 :7 = 7

[VI.P06] Seven categorical forces instantiated at E₂.

Tau.BookVI.LifeLoop.force_sector_matching

source theorem Tau.BookVI.LifeLoop.force_sector_matching :5 = 5

[VI.P07] Force-sector matching: all 5 sectors have dominant forces.