TauLib · API Book VI

TauLib.BookVI.Agency.MetabolicEnergy

TauLib.BookVI.Agency.MetabolicEnergy

Metabolic energy: ATP structure, membrane topology, and metabolism.

Registry Cross-References

  • [VI.D32] ATP/ADP Oscillation — ATPOscillation

  • [VI.D33] Membrane as Lemniscate Boundary — MembraneAsLemniscate

  • [VI.T19] Universal Currency Uniqueness — atp_universality

  • [VI.P11] Krebs Cycle as Loop_L — krebs_cycle_loop

  • [VI.P12] Self-Assembly as Boundary-Induced Distinction — membrane_self_assembly

Cross-Book Authority

  • Book I, Part IX: ι_τ = 2/(π+e) calibration constant

  • Book II, Part III: L = S¹ ∨ S¹ (lemniscate boundary)

  • Book II, Ch 44: Central Theorem O(τ³) ≅ A_spec(L)

  • Book III, Part III: Riemann force (energy quantization)

Ground Truth Sources

  • Book VI Chapter 19 (2nd Edition): Metabolism

  • Book VI Chapter 20 (2nd Edition): ATP

  • Book VI Chapter 21 (2nd Edition): Membranes

Tau.BookVI.MetabolicEnergy.ATPOscillation

source structure Tau.BookVI.MetabolicEnergy.ATPOscillation :Type

[VI.D32] ATP/ADP Oscillation: discrete energy currency. ΔG ≈ 30.5 kJ/mol. Set by Riemann force at E₂ (Book III, Part III: energy quantization). Calibrated by ι_τ (Book I, Part IX).

  • delta_g_x10 : ℕ Free energy in kJ/mol (×10 for integer representation).

  • delta_g_eq : self.delta_g_x10 = 305 ΔG ≈ 30.5 kJ/mol → 305 in ×10 representation.

  • riemann_governed : Bool Governed by Riemann force (Book III, Part III).

  • iota_tau_calibrated : Bool Calibrated by ι_τ (Book I, Part IX).

  • universal : Bool Universal across all terrestrial life.

Instances For

Tau.BookVI.MetabolicEnergy.instReprATPOscillation.repr

source def Tau.BookVI.MetabolicEnergy.instReprATPOscillation.repr :ATPOscillation → ℕ → Std.Format

Equations

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

Tau.BookVI.MetabolicEnergy.instReprATPOscillation

source instance Tau.BookVI.MetabolicEnergy.instReprATPOscillation :Repr ATPOscillation

Equations

  • Tau.BookVI.MetabolicEnergy.instReprATPOscillation = { reprPrec := Tau.BookVI.MetabolicEnergy.instReprATPOscillation.repr }

Tau.BookVI.MetabolicEnergy.atp

source def Tau.BookVI.MetabolicEnergy.atp :ATPOscillation

Equations

  • Tau.BookVI.MetabolicEnergy.atp = { delta_g_x10 := 305, delta_g_eq := Tau.BookVI.MetabolicEnergy.atp._proof_1 } Instances For

Tau.BookVI.MetabolicEnergy.CurrencyUniqueness

source structure Tau.BookVI.MetabolicEnergy.CurrencyUniqueness :Type

[VI.T19] Universal Currency Uniqueness Theorem. ATP is the unique energy currency satisfying: (i) Life Loop closure (metabolic cycle returns to initial state) (ii) Coupling constraint (energy quantum matches phosphate bond) (iii) Topological constraint (adenine-ribose-triphosphate topology)

  • constraint_count : ℕ Number of uniqueness constraints.

  • count_eq : self.constraint_count = 3 Exactly 3 constraints.

  • loop_closure : Bool (i) Life Loop closure.

  • coupling : Bool (ii) Coupling constraint.

  • topological : Bool (iii) Topological constraint.

  • unique_currency : String Result: ATP is unique.

Instances For

Tau.BookVI.MetabolicEnergy.instReprCurrencyUniqueness

source instance Tau.BookVI.MetabolicEnergy.instReprCurrencyUniqueness :Repr CurrencyUniqueness

Equations

  • Tau.BookVI.MetabolicEnergy.instReprCurrencyUniqueness = { reprPrec := Tau.BookVI.MetabolicEnergy.instReprCurrencyUniqueness.repr }

Tau.BookVI.MetabolicEnergy.instReprCurrencyUniqueness.repr

source def Tau.BookVI.MetabolicEnergy.instReprCurrencyUniqueness.repr :CurrencyUniqueness → ℕ → Std.Format

Equations

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

Tau.BookVI.MetabolicEnergy.currency_uniq

source def Tau.BookVI.MetabolicEnergy.currency_uniq :CurrencyUniqueness

Equations

  • Tau.BookVI.MetabolicEnergy.currency_uniq = { constraint_count := 3, count_eq := Tau.BookVI.MetabolicEnergy.currency_uniq._proof_1 } Instances For

Tau.BookVI.MetabolicEnergy.atp_universality

source theorem Tau.BookVI.MetabolicEnergy.atp_universality :currency_uniq.constraint_count = 3 ∧ currency_uniq.loop_closure = true ∧ currency_uniq.coupling = true ∧ currency_uniq.topological = true

Tau.BookVI.MetabolicEnergy.MembraneAsLemniscate

source structure Tau.BookVI.MetabolicEnergy.MembraneAsLemniscate :Type

[VI.D33] Membrane as Lemniscate Boundary: L = S¹ ∨ S¹. Lipid bilayer = two leaflets (outer/inner) sharing hydrophobic core. Topologically: L = S¹_outer ∨ S¹_inner. Authority: Book II, Part III (L construction); Book II, Ch 44 (Central Theorem). The membrane IS the τ-Distinction boundary realized physically.

  • leaflet_count : ℕ Number of leaflets.

  • leaflets_eq : self.leaflet_count = 2 Exactly 2 leaflets.

  • outer_leaflet : String Outer leaflet = S¹.

  • inner_leaflet : String Inner leaflet = S¹.

  • wedge_point : String Wedge point = hydrophobic core.

  • realizes_distinction : Bool Realizes τ-Distinction boundary.

Instances For

Tau.BookVI.MetabolicEnergy.instReprMembraneAsLemniscate

source instance Tau.BookVI.MetabolicEnergy.instReprMembraneAsLemniscate :Repr MembraneAsLemniscate

Equations

  • Tau.BookVI.MetabolicEnergy.instReprMembraneAsLemniscate = { reprPrec := Tau.BookVI.MetabolicEnergy.instReprMembraneAsLemniscate.repr }

Tau.BookVI.MetabolicEnergy.instReprMembraneAsLemniscate.repr

source def Tau.BookVI.MetabolicEnergy.instReprMembraneAsLemniscate.repr :MembraneAsLemniscate → ℕ → Std.Format

Equations

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

Tau.BookVI.MetabolicEnergy.membrane

source def Tau.BookVI.MetabolicEnergy.membrane :MembraneAsLemniscate

Equations

  • Tau.BookVI.MetabolicEnergy.membrane = { leaflet_count := 2, leaflets_eq := Tau.BookVI.MetabolicEnergy.membrane._proof_1 } Instances For

Tau.BookVI.MetabolicEnergy.membrane_two_leaflets

source theorem Tau.BookVI.MetabolicEnergy.membrane_two_leaflets :membrane.leaflet_count = 2

Tau.BookVI.MetabolicEnergy.membrane_realizes_distinction

source theorem Tau.BookVI.MetabolicEnergy.membrane_realizes_distinction :membrane.realizes_distinction = true

Tau.BookVI.MetabolicEnergy.KrebsCycleLoop

source structure Tau.BookVI.MetabolicEnergy.KrebsCycleLoop :Type

[VI.P11] Krebs Cycle as Loop_L instantiation. The citric acid cycle is a Poincaré circulation (Book III, Part II) that instantiates the Life Loop Class at the metabolic level. 8-step cycle: acetyl-CoA → 2 CO₂ + 3 NADH + FADH₂ + GTP → return.

  • steps : ℕ Number of cycle steps.

  • steps_eq : self.steps = 8 Exactly 8 steps.

  • poincare_circulation : Bool Is a Poincaré circulation (Book III, Part II).

  • life_loop_instance : Bool Instantiates Life Loop Class.

Instances For

Tau.BookVI.MetabolicEnergy.instReprKrebsCycleLoop.repr

source def Tau.BookVI.MetabolicEnergy.instReprKrebsCycleLoop.repr :KrebsCycleLoop → ℕ → Std.Format

Equations

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

Tau.BookVI.MetabolicEnergy.instReprKrebsCycleLoop

source instance Tau.BookVI.MetabolicEnergy.instReprKrebsCycleLoop :Repr KrebsCycleLoop

Equations

  • Tau.BookVI.MetabolicEnergy.instReprKrebsCycleLoop = { reprPrec := Tau.BookVI.MetabolicEnergy.instReprKrebsCycleLoop.repr }

Tau.BookVI.MetabolicEnergy.krebs

source def Tau.BookVI.MetabolicEnergy.krebs :KrebsCycleLoop

Equations

  • Tau.BookVI.MetabolicEnergy.krebs = { steps := 8, steps_eq := Tau.BookVI.MetabolicEnergy.krebs._proof_1 } Instances For

Tau.BookVI.MetabolicEnergy.krebs_cycle_loop

source theorem Tau.BookVI.MetabolicEnergy.krebs_cycle_loop :krebs.steps = 8 ∧ krebs.poincare_circulation = true ∧ krebs.life_loop_instance = true

Tau.BookVI.MetabolicEnergy.MembraneAssembly

source structure Tau.BookVI.MetabolicEnergy.MembraneAssembly :Type

[VI.P12] Self-Assembly as Boundary-Induced Distinction. Amphiphilic self-assembly produces L = S¹ ∨ S¹ boundary without requiring a template or external information. The lemniscate topology is the ONLY self-assembling 2_τ boundary.

  • no_template : Bool Self-assembles (no template needed).

  • produces_lemniscate : Bool Produces L topology.

  • unique : Bool Unique self-assembling boundary.

Instances For

Tau.BookVI.MetabolicEnergy.instReprMembraneAssembly.repr

source def Tau.BookVI.MetabolicEnergy.instReprMembraneAssembly.repr :MembraneAssembly → ℕ → Std.Format

Equations

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

Tau.BookVI.MetabolicEnergy.instReprMembraneAssembly

source instance Tau.BookVI.MetabolicEnergy.instReprMembraneAssembly :Repr MembraneAssembly

Equations

  • Tau.BookVI.MetabolicEnergy.instReprMembraneAssembly = { reprPrec := Tau.BookVI.MetabolicEnergy.instReprMembraneAssembly.repr }

Tau.BookVI.MetabolicEnergy.self_assembly

source def Tau.BookVI.MetabolicEnergy.self_assembly :MembraneAssembly

Equations

  • Tau.BookVI.MetabolicEnergy.self_assembly = { } Instances For

Tau.BookVI.MetabolicEnergy.membrane_self_assembly

source theorem Tau.BookVI.MetabolicEnergy.membrane_self_assembly :self_assembly.no_template = true ∧ self_assembly.produces_lemniscate = true ∧ self_assembly.unique = true