TauLib · API Book VI

TauLib.BookVI.Source.GeneticCode

TauLib.BookVI.Source.GeneticCode

Genetic code: codon structure, central dogma morphism, error minimization.

Registry Cross-References

  • [VI.D40] BSD Motivic Structure of Genetic Code — BSDGeneticCode

  • [VI.T22] Codon Degeneracy as Error Correction — codon_error_correction

  • [VI.P15] Central Dogma as Morphism Composition — central_dogma_morphism

  • [VI.T21] Turing Patterns as Hodge Eigenmodes — turing_hodge_eigenmodes

  • [VI.P14] Reaction-Diffusion from τ³ Structure — reaction_diffusion_tau3

Cross-Book Authority

  • Book III, Part V: BSD force (rank of rational points → code structure)

  • Book III, Part IV: Hodge force (Laplacian eigenmodes → morphogenesis)

  • Book II, Part II: τ³ = τ¹ ×_f T² (central dogma maps between factors)

  • Book II, Ch 116: τ-Hodge Theory (Hodge decomposition on τ³)

Ground Truth Sources

  • Book VI Chapter 26 (2nd Edition): Morphogenesis

  • Book VI Chapter 27 (2nd Edition): The Genetic Code

Tau.BookVI.GeneticCode.BSDGeneticCode

source structure Tau.BookVI.GeneticCode.BSDGeneticCode :Type

[VI.D40] BSD Motivic Structure of the Genetic Code. The 20 standard amino acids and 64 codons reflect BSD-force structure (Book III, Part V) on the carrier’s code space. Degeneracy pattern = error-correcting code.

  • amino_acids : ℕ Number of standard amino acids.

  • aa_eq : self.amino_acids = 20 Exactly 20.

  • codons : ℕ Number of codons.

  • codons_eq : self.codons = 64 Exactly 64 = 4³.

  • stop_codons : ℕ Stop codons.

  • stop_eq : self.stop_codons = 3 Exactly 3 stop codons.

  • bsd_connection : Bool Connected to BSD force (Book III, Part V).

Instances For

Tau.BookVI.GeneticCode.instReprBSDGeneticCode

source instance Tau.BookVI.GeneticCode.instReprBSDGeneticCode :Repr BSDGeneticCode

Equations

  • Tau.BookVI.GeneticCode.instReprBSDGeneticCode = { reprPrec := Tau.BookVI.GeneticCode.instReprBSDGeneticCode.repr }

Tau.BookVI.GeneticCode.instReprBSDGeneticCode.repr

source def Tau.BookVI.GeneticCode.instReprBSDGeneticCode.repr :BSDGeneticCode → ℕ → Std.Format

Equations

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Tau.BookVI.GeneticCode.genetic_code

source def Tau.BookVI.GeneticCode.genetic_code :BSDGeneticCode

Equations

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Tau.BookVI.GeneticCode.genetic_code_structure

source theorem Tau.BookVI.GeneticCode.genetic_code_structure :genetic_code.amino_acids = 20 ∧ genetic_code.codons = 64 ∧ genetic_code.stop_codons = 3

Tau.BookVI.GeneticCode.CodonErrorCorrection

source structure Tau.BookVI.GeneticCode.CodonErrorCorrection :Type

[VI.T22] Codon Degeneracy as Error Correction Theorem. Standard code in top 0.01% for error minimization (Freeland-Hurst). Redundancy: 1.68 bits/codon (log₂(64/20) ≈ 1.68). Established result from information theory + computational biology.

  • percentile_rank_x100 : ℕ Percentile rank for error minimization.

  • rank_eq : self.percentile_rank_x100 = 9999 Top 0.01% → 9999 out of 10000.

  • redundancy_x100 : ℕ Redundancy in bits/codon (×100 for integer).

  • redundancy_eq : self.redundancy_x100 = 168 1.68 bits → 168.

  • scope : String Scope: established (Shannon + Freeland-Hurst).

Instances For

Tau.BookVI.GeneticCode.instReprCodonErrorCorrection

source instance Tau.BookVI.GeneticCode.instReprCodonErrorCorrection :Repr CodonErrorCorrection

Equations

  • Tau.BookVI.GeneticCode.instReprCodonErrorCorrection = { reprPrec := Tau.BookVI.GeneticCode.instReprCodonErrorCorrection.repr }

Tau.BookVI.GeneticCode.instReprCodonErrorCorrection.repr

source def Tau.BookVI.GeneticCode.instReprCodonErrorCorrection.repr :CodonErrorCorrection → ℕ → Std.Format

Equations

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Tau.BookVI.GeneticCode.codon_err

source def Tau.BookVI.GeneticCode.codon_err :CodonErrorCorrection

Equations

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Tau.BookVI.GeneticCode.codon_error_correction

source theorem Tau.BookVI.GeneticCode.codon_error_correction :codon_err.percentile_rank_x100 = 9999 ∧ codon_err.redundancy_x100 = 168

Tau.BookVI.GeneticCode.CentralDogmaMorphism

source structure Tau.BookVI.GeneticCode.CentralDogmaMorphism :Type

[VI.P15] Central Dogma as Morphism Composition. DNA → mRNA → Protein maps between τ³ factors: τ¹_DNA → (τ¹ × T²)_mRNA → T²_Protein. Authority: Book II, Part II (τ³ = τ¹ ×_f T² factor structure).

  • steps : ℕ Number of morphism steps.

  • steps_eq : self.steps = 2 Exactly 2 steps (transcription + translation).

  • source_factor : String Source factor: τ¹ (DNA, temporal/base).

  • intermediate : String Intermediate: τ¹ × T² (mRNA, mixed).

  • target_factor : String Target factor: T² (Protein, fiber/spatial).

Instances For

Tau.BookVI.GeneticCode.instReprCentralDogmaMorphism.repr

source def Tau.BookVI.GeneticCode.instReprCentralDogmaMorphism.repr :CentralDogmaMorphism → ℕ → Std.Format

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Tau.BookVI.GeneticCode.instReprCentralDogmaMorphism

source instance Tau.BookVI.GeneticCode.instReprCentralDogmaMorphism :Repr CentralDogmaMorphism

Equations

  • Tau.BookVI.GeneticCode.instReprCentralDogmaMorphism = { reprPrec := Tau.BookVI.GeneticCode.instReprCentralDogmaMorphism.repr }

Tau.BookVI.GeneticCode.central_dogma

source def Tau.BookVI.GeneticCode.central_dogma :CentralDogmaMorphism

Equations

  • Tau.BookVI.GeneticCode.central_dogma = { steps := 2, steps_eq := Tau.BookVI.GeneticCode.central_dogma._proof_1 } Instances For

Tau.BookVI.GeneticCode.central_dogma_morphism

source theorem Tau.BookVI.GeneticCode.central_dogma_morphism :central_dogma.steps = 2 ∧ central_dogma.source_factor = “tau1_DNA” ∧ central_dogma.target_factor = “T2_Protein”

Tau.BookVI.GeneticCode.TuringHodgeEigenmodes

source structure Tau.BookVI.GeneticCode.TuringHodgeEigenmodes :Type

[VI.T21] Turing Patterns as Hodge Eigenmode Instantiations. Morphogenetic patterns = eigenfunctions of the Hodge Laplacian Δ_H. Reaction from τ¹ base, diffusion from T² fiber. Authority: Book III, Part IV (Hodge force); Book II, Ch 116 (τ-Hodge).

  • reaction_source : String Reaction source: τ¹ (base, temporal).

  • diffusion_domain : String Diffusion domain: T² (fiber, spatial).

  • hodge_laplacian : Bool Governed by Hodge Laplacian Δ_H.

  • scope : String Scope: τ-effective.

Instances For

Tau.BookVI.GeneticCode.instReprTuringHodgeEigenmodes

source instance Tau.BookVI.GeneticCode.instReprTuringHodgeEigenmodes :Repr TuringHodgeEigenmodes

Equations

  • Tau.BookVI.GeneticCode.instReprTuringHodgeEigenmodes = { reprPrec := Tau.BookVI.GeneticCode.instReprTuringHodgeEigenmodes.repr }

Tau.BookVI.GeneticCode.instReprTuringHodgeEigenmodes.repr

source def Tau.BookVI.GeneticCode.instReprTuringHodgeEigenmodes.repr :TuringHodgeEigenmodes → ℕ → Std.Format

Equations

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Tau.BookVI.GeneticCode.turing_hodge

source def Tau.BookVI.GeneticCode.turing_hodge :TuringHodgeEigenmodes

Equations

  • Tau.BookVI.GeneticCode.turing_hodge = { } Instances For

Tau.BookVI.GeneticCode.turing_hodge_eigenmodes

source theorem Tau.BookVI.GeneticCode.turing_hodge_eigenmodes :turing_hodge.hodge_laplacian = true ∧ turing_hodge.reaction_source = “tau1_base” ∧ turing_hodge.diffusion_domain = “T2_fiber”

Tau.BookVI.GeneticCode.ReactionDiffusionTau3

source structure Tau.BookVI.GeneticCode.ReactionDiffusionTau3 :Type

[VI.P14] Reaction-Diffusion from τ³ Structure. The fibered product τ³ = τ¹ ×_f T² naturally separates reaction (temporal, base) from diffusion (spatial, fiber). Authority: Book II, Part II (τ³ fibration).

  • reaction_is_base : Bool Reaction = base dynamics.

  • diffusion_is_fiber : Bool Diffusion = fiber dynamics.

  • tau3_separated : Bool Natural separation from τ³ structure.

Instances For

Tau.BookVI.GeneticCode.instReprReactionDiffusionTau3

source instance Tau.BookVI.GeneticCode.instReprReactionDiffusionTau3 :Repr ReactionDiffusionTau3

Equations

  • Tau.BookVI.GeneticCode.instReprReactionDiffusionTau3 = { reprPrec := Tau.BookVI.GeneticCode.instReprReactionDiffusionTau3.repr }

Tau.BookVI.GeneticCode.instReprReactionDiffusionTau3.repr

source def Tau.BookVI.GeneticCode.instReprReactionDiffusionTau3.repr :ReactionDiffusionTau3 → ℕ → Std.Format

Equations

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Tau.BookVI.GeneticCode.rxn_diff

source def Tau.BookVI.GeneticCode.rxn_diff :ReactionDiffusionTau3

Equations

  • Tau.BookVI.GeneticCode.rxn_diff = { } Instances For

Tau.BookVI.GeneticCode.reaction_diffusion_tau3

source theorem Tau.BookVI.GeneticCode.reaction_diffusion_tau3 :rxn_diff.reaction_is_base = true ∧ rxn_diff.diffusion_is_fiber = true ∧ rxn_diff.tau3_separated = true