TauLib · API Book VI

TauLib.BookVI.LifeCore.ParityBridge

TauLib.BookVI.LifeCore.ParityBridge

The Parity Bridge: E₁→E₂ transition factors uniquely through the weak sector. The polarity functional P_S tests whether a holonomy sector carries intrinsic parity asymmetry. Only the weak sector is nontrivial.

Registry Cross-References

  • [VI.D01] Polarity Functional — PolarityFunctional

  • [VI.D02] Polarity-Typed Two-Point Object (2_τ) — TwoPointObject

  • [VI.D03] Three Polarity Terms — ThreePolarityTerms

  • [VI.L01] Weak-Sector Uniqueness — weak_sector_uniqueness

  • [VI.T01] Parity Bridge Theorem — parity_bridge_theorem

  • [VI.P01] Low-Noise Carrier Condition — low_noise_carrier_condition

Ground Truth Sources

  • Book VI Chapter 3 (2nd Edition): The Parity Bridge

Tau.BookVI.ParityBridge.PolarityFunctional

source structure Tau.BookVI.ParityBridge.PolarityFunctional :Type

[VI.D01] Polarity functional: map P_S: End(S) → 2_τ testing whether a holonomy sector carries intrinsic parity asymmetry. Trivial for EM, Strong, Gravity; nontrivial uniquely for Weak.

  • sectors_tested : ℕ
  • nontrivial_count : ℕ
  • unique_nontrivial : self.nontrivial_count = 1
  • all_tested : self.sectors_tested = 4 Instances For

Tau.BookVI.ParityBridge.instReprPolarityFunctional.repr

source def Tau.BookVI.ParityBridge.instReprPolarityFunctional.repr :PolarityFunctional → ℕ → Std.Format

Equations

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

Tau.BookVI.ParityBridge.instReprPolarityFunctional

source instance Tau.BookVI.ParityBridge.instReprPolarityFunctional :Repr PolarityFunctional

Equations

  • Tau.BookVI.ParityBridge.instReprPolarityFunctional = { reprPrec := Tau.BookVI.ParityBridge.instReprPolarityFunctional.repr }

Tau.BookVI.ParityBridge.polarity_functional

source def Tau.BookVI.ParityBridge.polarity_functional :PolarityFunctional

Equations

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

Tau.BookVI.ParityBridge.TwoPointObject

source structure Tau.BookVI.ParityBridge.TwoPointObject :Type

[VI.D02] Polarity-typed two-point object 2_τ = {+, −}. Split-complex idempotent structure from lemniscate boundary.

  • point_count : ℕ
  • count_eq : self.point_count = 2
  • split_complex : Bool
  • from_lemniscate : Bool Instances For

Tau.BookVI.ParityBridge.instReprTwoPointObject.repr

source def Tau.BookVI.ParityBridge.instReprTwoPointObject.repr :TwoPointObject → ℕ → Std.Format

Equations

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

Tau.BookVI.ParityBridge.instReprTwoPointObject

source instance Tau.BookVI.ParityBridge.instReprTwoPointObject :Repr TwoPointObject

Equations

  • Tau.BookVI.ParityBridge.instReprTwoPointObject = { reprPrec := Tau.BookVI.ParityBridge.instReprTwoPointObject.repr }

Tau.BookVI.ParityBridge.two_point

source def Tau.BookVI.ParityBridge.two_point :TwoPointObject

Equations

  • Tau.BookVI.ParityBridge.two_point = { point_count := 2, count_eq := Tau.BookVI.ParityBridge.two_point._proof_1 } Instances For

Tau.BookVI.ParityBridge.ThreePolarityTerms

source structure Tau.BookVI.ParityBridge.ThreePolarityTerms :Type

[VI.D03] Three polarity terms: source, basin, stabilizer.

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

Tau.BookVI.ParityBridge.instReprThreePolarityTerms.repr

source def Tau.BookVI.ParityBridge.instReprThreePolarityTerms.repr :ThreePolarityTerms → ℕ → Std.Format

Equations

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

Tau.BookVI.ParityBridge.instReprThreePolarityTerms

source instance Tau.BookVI.ParityBridge.instReprThreePolarityTerms :Repr ThreePolarityTerms

Equations

  • Tau.BookVI.ParityBridge.instReprThreePolarityTerms = { reprPrec := Tau.BookVI.ParityBridge.instReprThreePolarityTerms.repr }

Tau.BookVI.ParityBridge.polarity_terms

source def Tau.BookVI.ParityBridge.polarity_terms :ThreePolarityTerms

Equations

  • Tau.BookVI.ParityBridge.polarity_terms = { term_count := 3, count_eq := Tau.BookVI.ParityBridge.polarity_terms._proof_1 } Instances For

Tau.BookVI.ParityBridge.weak_sector_uniqueness

source theorem Tau.BookVI.ParityBridge.weak_sector_uniqueness :polarity_functional.nontrivial_count = 1 ∧ polarity_functional.sectors_tested = 4

[VI.L01] Weak-sector uniqueness: among 4 primitive sectors, weak is the unique one with nontrivial polarity.

Tau.BookVI.ParityBridge.ParityBridgeTheorem

source structure Tau.BookVI.ParityBridge.ParityBridgeTheorem :Type

[VI.T01] Parity Bridge Theorem: E₁→E₂ factors uniquely through weak sector. E₁ →[P_weak] 2_τ →[SelfDesc] E₂.

  • path_count : ℕ
  • unique_path : self.path_count = 1
  • source_layer : String
  • target_layer : String
  • mediating_sector : String Instances For

Tau.BookVI.ParityBridge.instReprParityBridgeTheorem.repr

source def Tau.BookVI.ParityBridge.instReprParityBridgeTheorem.repr :ParityBridgeTheorem → ℕ → Std.Format

Equations

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

Tau.BookVI.ParityBridge.instReprParityBridgeTheorem

source instance Tau.BookVI.ParityBridge.instReprParityBridgeTheorem :Repr ParityBridgeTheorem

Equations

  • Tau.BookVI.ParityBridge.instReprParityBridgeTheorem = { reprPrec := Tau.BookVI.ParityBridge.instReprParityBridgeTheorem.repr }

Tau.BookVI.ParityBridge.parity_bridge

source def Tau.BookVI.ParityBridge.parity_bridge :ParityBridgeTheorem

Equations

  • Tau.BookVI.ParityBridge.parity_bridge = { path_count := 1, unique_path := Tau.BookVI.ParityBridge.polarity_functional._proof_1 } Instances For

Tau.BookVI.ParityBridge.parity_bridge_theorem

source theorem Tau.BookVI.ParityBridge.parity_bridge_theorem :parity_bridge.path_count = 1

Tau.BookVI.ParityBridge.LowNoiseCarrierCondition

source structure Tau.BookVI.ParityBridge.LowNoiseCarrierCondition :Type

[VI.P01] Low-noise carrier condition: 3 conditions for E₁→E₂ transition.

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

Tau.BookVI.ParityBridge.instReprLowNoiseCarrierCondition

source instance Tau.BookVI.ParityBridge.instReprLowNoiseCarrierCondition :Repr LowNoiseCarrierCondition

Equations

  • Tau.BookVI.ParityBridge.instReprLowNoiseCarrierCondition = { reprPrec := Tau.BookVI.ParityBridge.instReprLowNoiseCarrierCondition.repr }

Tau.BookVI.ParityBridge.instReprLowNoiseCarrierCondition.repr

source def Tau.BookVI.ParityBridge.instReprLowNoiseCarrierCondition.repr :LowNoiseCarrierCondition → ℕ → Std.Format

Equations

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

Tau.BookVI.ParityBridge.low_noise

source def Tau.BookVI.ParityBridge.low_noise :LowNoiseCarrierCondition

Equations

  • Tau.BookVI.ParityBridge.low_noise = { condition_count := 3, count_eq := Tau.BookVI.ParityBridge.polarity_terms._proof_1 } Instances For

Tau.BookVI.ParityBridge.low_noise_carrier_condition

source theorem Tau.BookVI.ParityBridge.low_noise_carrier_condition :low_noise.condition_count = 3

Tau.BookVI.ParityBridge.PolarityPropagation

source structure Tau.BookVI.ParityBridge.PolarityPropagation :Type

[VI.D71] Polarity Propagation: functor mapping IV.D112 σ_A-admissibility through VI.T01 Parity Bridge into VI.D01 polarity functional. The propagation chain is: weak-sector parity violation (σ = C_τ, IV.T146) → Parity Bridge (VI.T01) → polarity functional P_weak (VI.D01) → biological chirality seed.

  • source_sector : String Source: weak-sector parity violation.

  • bridge_path_count : ℕ Bridge: VI.T01 unique factorization.

  • bridge_unique : self.bridge_path_count = 1

  • target_codomain : String Target: polarity functional output in 2_τ.

  • sign_preserved : Bool Propagation preserves chirality sign.

Instances For

Tau.BookVI.ParityBridge.instReprPolarityPropagation.repr

source def Tau.BookVI.ParityBridge.instReprPolarityPropagation.repr :PolarityPropagation → ℕ → Std.Format

Equations

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

Tau.BookVI.ParityBridge.instReprPolarityPropagation

source instance Tau.BookVI.ParityBridge.instReprPolarityPropagation :Repr PolarityPropagation

Equations

  • Tau.BookVI.ParityBridge.instReprPolarityPropagation = { reprPrec := Tau.BookVI.ParityBridge.instReprPolarityPropagation.repr }

Tau.BookVI.ParityBridge.polarity_propagation

source def Tau.BookVI.ParityBridge.polarity_propagation :PolarityPropagation

Equations

  • Tau.BookVI.ParityBridge.polarity_propagation = { bridge_path_count := 1, bridge_unique := Tau.BookVI.ParityBridge.polarity_functional._proof_1 } Instances For

Tau.BookVI.ParityBridge.ChiralitySeed

source structure Tau.BookVI.ParityBridge.ChiralitySeed :Type

[VI.D72] Chirality Seed: initial asymmetry from weak parity violation. The weak sector couples exclusively to left-handed fermions (V(A)=100%), seeding a universal directional bias. The seed magnitude is ~10⁻¹⁷ eV but the sign is coherent across all chiral molecules.

  • va_coupling_pct : ℕ Parity violation is maximal (100%) in weak sector.

  • va_maximal : self.va_coupling_pct = 100

  • coherent : Bool Seed is coherent: same sign for all amino acids.

  • iv_t146_source : Bool Source: IV.T146 σ = C_τ (Majorana).

Instances For

Tau.BookVI.ParityBridge.instReprChiralitySeed

source instance Tau.BookVI.ParityBridge.instReprChiralitySeed :Repr ChiralitySeed

Equations

  • Tau.BookVI.ParityBridge.instReprChiralitySeed = { reprPrec := Tau.BookVI.ParityBridge.instReprChiralitySeed.repr }

Tau.BookVI.ParityBridge.instReprChiralitySeed.repr

source def Tau.BookVI.ParityBridge.instReprChiralitySeed.repr :ChiralitySeed → ℕ → Std.Format

Equations

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

Tau.BookVI.ParityBridge.chirality_seed

source def Tau.BookVI.ParityBridge.chirality_seed :ChiralitySeed

Equations

  • Tau.BookVI.ParityBridge.chirality_seed = { va_coupling_pct := 100, va_maximal := Tau.BookVI.ParityBridge.chirality_seed._proof_1 } Instances For

Tau.BookVI.ParityBridge.propagation_preserves_chirality

source theorem Tau.BookVI.ParityBridge.propagation_preserves_chirality :polarity_propagation.sign_preserved = true ∧ polarity_propagation.bridge_path_count = 1 ∧ chirality_seed.va_coupling_pct = 100 ∧ chirality_seed.coherent = true

[VI.T41] Propagation Preserves Chirality: left-handed input through the Parity Bridge yields a definite polarity sign in 2_τ. Proof chain: weak-sector parity violation (ChiralitySeed, VI.D72) → unique bridge path (PolarityPropagation, VI.D71) → definite polarity (PolarityFunctional, VI.D01).

Tau.BookVI.ParityBridge.propagation_uniqueness

source theorem Tau.BookVI.ParityBridge.propagation_uniqueness :polarity_functional.nontrivial_count = 1 ∧ polarity_propagation.bridge_path_count = 1

[VI.L14] Propagation Uniqueness: weak-sector uniqueness (VI.L01) implies the propagation path is unique. Since only one sector has nontrivial polarity, there is exactly one route from parity violation to chirality seed.