TauLib · API Book VI

TauLib.BookVI.Consumer.FiberRegime

TauLib.BookVI.Consumer.FiberRegime

Fiber-enabled regime: eukaryotic innovations and multicellularity.

Registry Cross-References

  • [VI.D47] Fiber-Enabled Regime — FiberEnabledRegime

  • [VI.R19] 1st Edition Correction (mixer placement) — FirstEdCorrection

  • [VI.D48] Multicellularity as Colimit — MulticellularityColimit

  • [VI.P18] Development as Controlled Differentiation — DevelopmentDifferentiation

Cross-Book Authority

  • Book I, Part VII: colimits (universal constructions)

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

  • Book II, Part X: ω-germ code (profinite completion)

Ground Truth Sources

  • Book VI Chapter 34 (2nd Edition): Eukarya — The Fiber-Enabled Regime

  • Book VI Chapter 35 (2nd Edition): The Cell Cycle

Tau.BookVI.FiberRegime.FiberEnabledRegime

source structure Tau.BookVI.FiberRegime.FiberEnabledRegime :Type

[VI.D47] Fiber-Enabled Regime: eukaryotic compartmentalization unlocked by mixed-sector access to both fiber generators. Four key innovations: nucleus, mitochondria, endomembrane, cytoskeleton.

  • compartmentalization : Bool Full compartmentalization achieved.

  • innovation_count : ℕ Number of key innovations.

  • count_eq : self.innovation_count = 4 Exactly 4 innovations.

  • nucleus : Bool Innovation 1: nuclear envelope.

  • mitochondria : Bool Innovation 2: mitochondria (endosymbiosis).

  • endomembrane : Bool Innovation 3: endomembrane system.

  • cytoskeleton : Bool Innovation 4: cytoskeleton.

Instances For

Tau.BookVI.FiberRegime.instReprFiberEnabledRegime.repr

source def Tau.BookVI.FiberRegime.instReprFiberEnabledRegime.repr :FiberEnabledRegime → ℕ → Std.Format

Equations

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

Tau.BookVI.FiberRegime.instReprFiberEnabledRegime

source instance Tau.BookVI.FiberRegime.instReprFiberEnabledRegime :Repr FiberEnabledRegime

Equations

  • Tau.BookVI.FiberRegime.instReprFiberEnabledRegime = { reprPrec := Tau.BookVI.FiberRegime.instReprFiberEnabledRegime.repr }

Tau.BookVI.FiberRegime.fiber_regime

source def Tau.BookVI.FiberRegime.fiber_regime :FiberEnabledRegime

Equations

  • Tau.BookVI.FiberRegime.fiber_regime = { innovation_count := 4, count_eq := Tau.BookVI.FiberRegime.fiber_regime._proof_1 } Instances For

Tau.BookVI.FiberRegime.fiber_regime_four_innovations

source theorem Tau.BookVI.FiberRegime.fiber_regime_four_innovations :fiber_regime.innovation_count = 4 ∧ fiber_regime.compartmentalization = true

Tau.BookVI.FiberRegime.FirstEdCorrection

source structure Tau.BookVI.FiberRegime.FirstEdCorrection :Type

[VI.R19] 1st Edition Correction: mixer placement. 1st Ed paired (α, π) for consumer; 2nd Ed corrects to (π’, π’’). The mixed sector requires both fiber generators, not base generators.

  • old_pairing : String Old (incorrect) pairing.

  • new_pairing : String New (correct) pairing.

  • rationale : String Correction rationale: fiber generators required.

Instances For

Tau.BookVI.FiberRegime.instReprFirstEdCorrection.repr

source def Tau.BookVI.FiberRegime.instReprFirstEdCorrection.repr :FirstEdCorrection → ℕ → Std.Format

Equations

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

Tau.BookVI.FiberRegime.instReprFirstEdCorrection

source instance Tau.BookVI.FiberRegime.instReprFirstEdCorrection :Repr FirstEdCorrection

Equations

  • Tau.BookVI.FiberRegime.instReprFirstEdCorrection = { reprPrec := Tau.BookVI.FiberRegime.instReprFirstEdCorrection.repr }

Tau.BookVI.FiberRegime.correction_r19

source def Tau.BookVI.FiberRegime.correction_r19 :FirstEdCorrection

Equations

  • Tau.BookVI.FiberRegime.correction_r19 = { } Instances For

Tau.BookVI.FiberRegime.correction_changes_pairing

source theorem Tau.BookVI.FiberRegime.correction_changes_pairing :correction_r19.old_pairing ≠ correction_r19.new_pairing

Tau.BookVI.FiberRegime.MulticellularityColimit

source structure Tau.BookVI.FiberRegime.MulticellularityColimit :Type

[VI.D48] Multicellularity as Colimit (Book I, Part VII). A multicellular organism is a colimit over a diagram of cooperating cell types. The colimit construction ensures universal properties: any compatible morphism factors through it.

  • cell_count : ℕ Minimum cell count for multicellularity.

  • multi : self.cell_count ≥ 2 At least 2 cells.

  • cooperative : Bool Cells are cooperative (not parasitic).

  • colimit_construction : Bool Construction is a categorical colimit.

Instances For

Tau.BookVI.FiberRegime.instReprMulticellularityColimit.repr

source def Tau.BookVI.FiberRegime.instReprMulticellularityColimit.repr :MulticellularityColimit → ℕ → Std.Format

Equations

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

Tau.BookVI.FiberRegime.instReprMulticellularityColimit

source instance Tau.BookVI.FiberRegime.instReprMulticellularityColimit :Repr MulticellularityColimit

Equations

  • Tau.BookVI.FiberRegime.instReprMulticellularityColimit = { reprPrec := Tau.BookVI.FiberRegime.instReprMulticellularityColimit.repr }

Tau.BookVI.FiberRegime.multicellular

source def Tau.BookVI.FiberRegime.multicellular :MulticellularityColimit

Equations

  • Tau.BookVI.FiberRegime.multicellular = { cell_count := 2, multi := Tau.BookVI.FiberRegime.multicellular._proof_1 } Instances For

Tau.BookVI.FiberRegime.multicellularity_as_colimit

source theorem Tau.BookVI.FiberRegime.multicellularity_as_colimit :multicellular.cell_count ≥ 2 ∧ multicellular.cooperative = true ∧ multicellular.colimit_construction = true

Tau.BookVI.FiberRegime.DevelopmentDifferentiation

source structure Tau.BookVI.FiberRegime.DevelopmentDifferentiation :Type

[VI.P18] Development as Controlled Differentiation. Embryonic development is a refinement tower: totipotent → pluripotent → multipotent → unipotent → terminal. Each step is a controlled restriction of the ω-germ code (Book II, Part X).

  • refinement_tower : Bool Development proceeds via refinement tower.

  • potency_hierarchy : Bool Potency hierarchy exists (totipotent → terminal).

  • potency_levels : ℕ Number of potency levels.

  • levels_eq : self.potency_levels = 5 5 levels: totipotent, pluripotent, multipotent, unipotent, terminal.

Instances For

Tau.BookVI.FiberRegime.instReprDevelopmentDifferentiation

source instance Tau.BookVI.FiberRegime.instReprDevelopmentDifferentiation :Repr DevelopmentDifferentiation

Equations

  • Tau.BookVI.FiberRegime.instReprDevelopmentDifferentiation = { reprPrec := Tau.BookVI.FiberRegime.instReprDevelopmentDifferentiation.repr }

Tau.BookVI.FiberRegime.instReprDevelopmentDifferentiation.repr

source def Tau.BookVI.FiberRegime.instReprDevelopmentDifferentiation.repr :DevelopmentDifferentiation → ℕ → Std.Format

Equations

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

Tau.BookVI.FiberRegime.development

source def Tau.BookVI.FiberRegime.development :DevelopmentDifferentiation

Equations

  • Tau.BookVI.FiberRegime.development = { potency_levels := 5, levels_eq := Tau.BookVI.FiberRegime.development._proof_1 } Instances For

Tau.BookVI.FiberRegime.development_refinement

source theorem Tau.BookVI.FiberRegime.development_refinement :development.refinement_tower = true ∧ development.potency_hierarchy = true ∧ development.potency_levels = 5