TauLib · API Book VI

TauLib.BookVI.Consumer.ConsumerMixer

TauLib.BookVI.Consumer.ConsumerMixer

Consumer mixer on (π’, π’’): the mixed-sector foundation of animal life.

Registry Cross-References

  • [VI.D46] Consumer Mixer on (π’, π’’) — ConsumerMixer

  • [VI.T25] Signature Rigidity Determines Uniqueness — signature_rigidity_uniqueness

  • [VI.L07] Consumer as Bridge-Head to E₃ — bridge_head_e3

Cross-Book Authority

  • Book I, Part I: generators α, π, π’, π’’ (five generators of τ³)

  • Book II, Part II: π₁(T²) ≅ ℤ × ℤ (fiber fundamental group, two winding numbers)

  • Book VI, Part 1: VI.D20 consumer sector (mixed sector in 4+1 classification)

Ground Truth Sources

  • Book VI Chapter 33 (2nd Edition): The Consumer Mixer

Tau.BookVI.Consumer.ConsumerMixer

source structure Tau.BookVI.Consumer.ConsumerMixer :Type

[VI.D46] Consumer Mixer on (π’, π’’): mixed-sector pairing of both fiber generators. The only non-primitive sector. Generator pair: (π’, π’’) on fiber T² (Book I, Part I). Winding: π₁(T²) ≅ ℤ × ℤ gives two independent winding numbers (Book II, Part II). Both must be nontrivial.

  • generator_pair : String Generator pair label.

  • is_mixed : Bool Mixed sector (not primitive).

  • winding_pi_prime : ℕ Winding number on π’ (must be ≥ 1).

  • winding_pi_double : ℕ Winding number on π’’ (must be ≥ 1).

  • pi_prime_nontrivial : self.winding_pi_prime ≥ 1 π’ winding nontrivial.

  • pi_double_nontrivial : self.winding_pi_double ≥ 1 π’’ winding nontrivial.

Instances For

Tau.BookVI.Consumer.instReprConsumerMixer.repr

source def Tau.BookVI.Consumer.instReprConsumerMixer.repr :ConsumerMixer → ℕ → Std.Format

Equations

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

Tau.BookVI.Consumer.instReprConsumerMixer

source instance Tau.BookVI.Consumer.instReprConsumerMixer :Repr ConsumerMixer

Equations

  • Tau.BookVI.Consumer.instReprConsumerMixer = { reprPrec := Tau.BookVI.Consumer.instReprConsumerMixer.repr }

Tau.BookVI.Consumer.canonical_mixer

source def Tau.BookVI.Consumer.canonical_mixer :ConsumerMixer

Equations

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

Tau.BookVI.Consumer.consumer_is_mixed_sector

source theorem Tau.BookVI.Consumer.consumer_is_mixed_sector :FourPlusOne.consumer_sector.is_primitive = false ∧ canonical_mixer.is_mixed = true

Consumer is the mixed sector from FourPlusOne.

Tau.BookVI.Consumer.consumer_generator_match

source theorem Tau.BookVI.Consumer.consumer_generator_match :canonical_mixer.generator_pair = FourPlusOne.consumer_sector.generator

Consumer matches FourPlusOne generator label.

Tau.BookVI.Consumer.SignatureRigidity

source structure Tau.BookVI.Consumer.SignatureRigidity :Type

[VI.T25] Signature Rigidity Determines Uniqueness. Among the 10 possible generator pairings on τ³:

  • base–base (α,π): both base → no fiber innovation → unstable

  • base–fiber (α,π’) etc.: mixed base+fiber → partial → unstable

  • fiber–fiber (π’,π’’): both fiber generators → full T² coverage → stable Only (π’,π’’) yields a stable mixed sector.

  • total_pairings : ℕ Total possible pairings from 5 generators taken 2.

  • base_base_stable : Bool Only fiber–fiber is stable.

  • base_fiber_stable : Bool Base–fiber pairings unstable.

  • fiber_fiber_stable : Bool Fiber–fiber pairing stable (π’,π’’ only).

  • stable_count : ℕ Stable pairings count.

  • stable_eq : self.stable_count = 1 Exactly 1 stable pairing.

Instances For

Tau.BookVI.Consumer.instReprSignatureRigidity.repr

source def Tau.BookVI.Consumer.instReprSignatureRigidity.repr :SignatureRigidity → ℕ → Std.Format

Equations

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

Tau.BookVI.Consumer.instReprSignatureRigidity

source instance Tau.BookVI.Consumer.instReprSignatureRigidity :Repr SignatureRigidity

Equations

  • Tau.BookVI.Consumer.instReprSignatureRigidity = { reprPrec := Tau.BookVI.Consumer.instReprSignatureRigidity.repr }

Tau.BookVI.Consumer.sig_rigid

source def Tau.BookVI.Consumer.sig_rigid :SignatureRigidity

Equations

  • Tau.BookVI.Consumer.sig_rigid = { total_pairings := 10, stable_count := 1, stable_eq := Tau.BookVI.Consumer.sig_rigid._proof_1 } Instances For

Tau.BookVI.Consumer.signature_rigidity_uniqueness

source theorem Tau.BookVI.Consumer.signature_rigidity_uniqueness :sig_rigid.fiber_fiber_stable = true ∧ sig_rigid.base_base_stable = false ∧ sig_rigid.base_fiber_stable = false ∧ sig_rigid.stable_count = 1

Tau.BookVI.Consumer.BridgeHeadE3

source structure Tau.BookVI.Consumer.BridgeHeadE3 :Type

[VI.L07] Consumer as Bridge-Head to E₃. Only the mixed sector supports Eval² = Eval ∘ Eval (second-order self-description). This opens the bridge from E₂ (life) to E₃ (consciousness/mind). Primitive sectors have Eval¹ only.

  • eval_order : ℕ Evaluator order (2 = second-order self-description).

  • order_eq : self.eval_order = 2 Exactly order 2.

  • only_mixed_sector : Bool Only mixed sector reaches E₃.

  • opens_e3 : Bool Opens enrichment layer E₃.

Instances For

Tau.BookVI.Consumer.instReprBridgeHeadE3

source instance Tau.BookVI.Consumer.instReprBridgeHeadE3 :Repr BridgeHeadE3

Equations

  • Tau.BookVI.Consumer.instReprBridgeHeadE3 = { reprPrec := Tau.BookVI.Consumer.instReprBridgeHeadE3.repr }

Tau.BookVI.Consumer.instReprBridgeHeadE3.repr

source def Tau.BookVI.Consumer.instReprBridgeHeadE3.repr :BridgeHeadE3 → ℕ → Std.Format

Equations

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

Tau.BookVI.Consumer.bridge_head

source def Tau.BookVI.Consumer.bridge_head :BridgeHeadE3

Equations

  • Tau.BookVI.Consumer.bridge_head = { eval_order := 2, order_eq := Tau.BookVI.Consumer.bridge_head._proof_1 } Instances For

Tau.BookVI.Consumer.bridge_head_e3

source theorem Tau.BookVI.Consumer.bridge_head_e3 :bridge_head.eval_order = 2 ∧ bridge_head.only_mixed_sector = true ∧ bridge_head.opens_e3 = true