TauLib · API Book VI

TauLib.BookVI.Closure.Ecosystem

TauLib.BookVI.Closure.Ecosystem

Ecosystems: inter-sector web, biogeochemical circulation, repair budget.

Registry Cross-References

  • [VI.D44] Inter-Sector Web — InterSectorWeb

  • [VI.D45] Repair Budget — RepairBudget

  • [VI.T24] Ecosystem as Multi-Scale Poincaré Circulation — ecosystem_poincare

  • [VI.P17] Metamorphosis Preserves SelfDesc — metamorphosis_selfdesc

Cross-Book Authority

  • Book III, Part II: Poincaré force (periodic orbits → biogeochemical cycles)

  • Book I, Part VII: Colimits (categorical universal construction → lichen)

Ground Truth Sources

  • Book VI Chapter 31 (2nd Edition): Symbiosis and Ecosystems

  • Book VI Chapter 32 (2nd Edition): Healing, Regeneration, and Repair

Tau.BookVI.Ecosystem.InterSectorWeb

source structure Tau.BookVI.Ecosystem.InterSectorWeb :Type

[VI.D44] Inter-Sector Web: coupling graph between Life sectors. Each sector (persistence, agency, source, closure, consumer) is a node; edges represent inter-sector metabolic or informational coupling. Every ecosystem is an Inter-Sector Web.

  • sector_count : ℕ Number of sector nodes.

  • count_eq : self.sector_count = 5 Exactly 5 sectors.

  • connected : Bool Web is connected (every sector couples to at least one other).

  • source_closure_dual : Bool Source-closure duality: these two sectors are always coupled.

Instances For

Tau.BookVI.Ecosystem.instReprInterSectorWeb

source instance Tau.BookVI.Ecosystem.instReprInterSectorWeb :Repr InterSectorWeb

Equations

  • Tau.BookVI.Ecosystem.instReprInterSectorWeb = { reprPrec := Tau.BookVI.Ecosystem.instReprInterSectorWeb.repr }

Tau.BookVI.Ecosystem.instReprInterSectorWeb.repr

source def Tau.BookVI.Ecosystem.instReprInterSectorWeb.repr :InterSectorWeb → ℕ → Std.Format

Equations

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

Tau.BookVI.Ecosystem.isw

source def Tau.BookVI.Ecosystem.isw :InterSectorWeb

Equations

  • Tau.BookVI.Ecosystem.isw = { sector_count := 5, count_eq := Tau.BookVI.Ecosystem.isw._proof_1 } Instances For

Tau.BookVI.Ecosystem.inter_sector_web_five

source theorem Tau.BookVI.Ecosystem.inter_sector_web_five :isw.sector_count = 5

Tau.BookVI.Ecosystem.inter_sector_web_connected

source theorem Tau.BookVI.Ecosystem.inter_sector_web_connected :isw.connected = true ∧ isw.source_closure_dual = true

Tau.BookVI.Ecosystem.EcosystemPoincare

source structure Tau.BookVI.Ecosystem.EcosystemPoincare :Type

[VI.T24] Ecosystem as Multi-Scale Poincaré Circulation. Every biogeochemical element traces a closed orbit in the inter-sector coupling graph. This is Poincaré circulation (Book III, Part II) at the ecosystem scale. Examples: carbon cycle, nitrogen cycle (6 steps), water cycle.

  • major_cycles : ℕ Number of major biogeochemical cycles formalized.

  • cycles_ge : self.major_cycles ≥ 3 At least 3 (C, N, H₂O).

  • all_closed : Bool All cycles are closed (Poincaré circulation).

  • multi_scale : Bool Multi-scale: cell → organism → ecosystem.

  • poincare_authority : Bool Authority: Book III, Part II (Poincaré force).

Instances For

Tau.BookVI.Ecosystem.instReprEcosystemPoincare.repr

source def Tau.BookVI.Ecosystem.instReprEcosystemPoincare.repr :EcosystemPoincare → ℕ → Std.Format

Equations

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

Tau.BookVI.Ecosystem.instReprEcosystemPoincare

source instance Tau.BookVI.Ecosystem.instReprEcosystemPoincare :Repr EcosystemPoincare

Equations

  • Tau.BookVI.Ecosystem.instReprEcosystemPoincare = { reprPrec := Tau.BookVI.Ecosystem.instReprEcosystemPoincare.repr }

Tau.BookVI.Ecosystem.eco_poincare

source def Tau.BookVI.Ecosystem.eco_poincare :EcosystemPoincare

Equations

  • Tau.BookVI.Ecosystem.eco_poincare = { major_cycles := 3, cycles_ge := Tau.BookVI.Ecosystem.eco_poincare._proof_1 } Instances For

Tau.BookVI.Ecosystem.ecosystem_poincare

source theorem Tau.BookVI.Ecosystem.ecosystem_poincare :eco_poincare.major_cycles ≥ 3 ∧ eco_poincare.all_closed = true ∧ eco_poincare.multi_scale = true

Tau.BookVI.Ecosystem.RepairBudget

source structure Tau.BookVI.Ecosystem.RepairBudget :Type

[VI.D45] Repair Budget: finite resource for SelfDesc maintenance. R_max = maximum cumulative repair before defect overwhelms. Connects to SelfDesc Closure Theorem (VI.T03): perturbations within basin are corrected, but R_max bounds the basin.

  • finite_budget : Bool Budget is finite for finite-lineage carriers.

  • bounds_basin : Bool Budget bounds the SelfDesc basin.

  • selfdesc_connection : Bool Connects to SelfDesc Closure (VI.T03).

Instances For

Tau.BookVI.Ecosystem.instReprRepairBudget

source instance Tau.BookVI.Ecosystem.instReprRepairBudget :Repr RepairBudget

Equations

  • Tau.BookVI.Ecosystem.instReprRepairBudget = { reprPrec := Tau.BookVI.Ecosystem.instReprRepairBudget.repr }

Tau.BookVI.Ecosystem.instReprRepairBudget.repr

source def Tau.BookVI.Ecosystem.instReprRepairBudget.repr :RepairBudget → ℕ → Std.Format

Equations

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

Tau.BookVI.Ecosystem.repair_budget

source def Tau.BookVI.Ecosystem.repair_budget :RepairBudget

Equations

  • Tau.BookVI.Ecosystem.repair_budget = { } Instances For

Tau.BookVI.Ecosystem.repair_budget_finite

source theorem Tau.BookVI.Ecosystem.repair_budget_finite :repair_budget.finite_budget = true ∧ repair_budget.bounds_basin = true

Tau.BookVI.Ecosystem.MetamorphosisSelfDesc

source structure Tau.BookVI.Ecosystem.MetamorphosisSelfDesc :Type

[VI.P17] Metamorphosis Preserves SelfDesc. ω-germ codes are identical in larva and adult; SelfDesc holds at every instant of metamorphosis. The code is a profinite invariant (Book II, Part X) that persists through substrate replacement.

  • code_preserved : Bool ω-germ code preserved across metamorphosis.

  • selfdesc_continuous : Bool SelfDesc holds at every instant.

  • profinite_invariant : Bool Code is profinite invariant (Book II, Part X).

Instances For

Tau.BookVI.Ecosystem.instReprMetamorphosisSelfDesc.repr

source def Tau.BookVI.Ecosystem.instReprMetamorphosisSelfDesc.repr :MetamorphosisSelfDesc → ℕ → Std.Format

Equations

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

Tau.BookVI.Ecosystem.instReprMetamorphosisSelfDesc

source instance Tau.BookVI.Ecosystem.instReprMetamorphosisSelfDesc :Repr MetamorphosisSelfDesc

Equations

  • Tau.BookVI.Ecosystem.instReprMetamorphosisSelfDesc = { reprPrec := Tau.BookVI.Ecosystem.instReprMetamorphosisSelfDesc.repr }

Tau.BookVI.Ecosystem.metamorphosis

source def Tau.BookVI.Ecosystem.metamorphosis :MetamorphosisSelfDesc

Equations

  • Tau.BookVI.Ecosystem.metamorphosis = { } Instances For

Tau.BookVI.Ecosystem.metamorphosis_selfdesc

source theorem Tau.BookVI.Ecosystem.metamorphosis_selfdesc :metamorphosis.code_preserved = true ∧ metamorphosis.selfdesc_continuous = true ∧ metamorphosis.profinite_invariant = true