TauLib · API Book VI

TauLib.BookVI.Consumer.Identity

TauLib.BookVI.Consumer.Identity

Identity over code, not carrier: Ship of Theseus resolution.

Registry Cross-References

  • [VI.D53] SelfDesc over Code, Not Carrier — SelfDescOverCode

  • [VI.L08] Substrate Replacement Preserves Life-Equivalence — substrate_replacement_preserves_life

Cross-Book Authority

  • Book II, Part X: ω-germ code (profinite invariant, identity criterion)

  • Book I, Part I: generators of τ³ (code is over generators, not material substrate)

Ground Truth Sources

  • Book VI Chapter 42 (2nd Edition): The Ship of Theseus

Tau.BookVI.Identity.SelfDescOverCode

source structure Tau.BookVI.Identity.SelfDescOverCode :Type

[VI.D53] SelfDesc over Code, Not Carrier. Biological identity resides in the ω-germ code (Book II, Part X), not in the material carrier. The profinite invariant is preserved under complete material turnover.

  • identity_locus : String Identity locus is the ω-germ code.

  • not_carrier : Bool Identity is NOT in the carrier.

  • profinite_invariant : Bool The ω-germ code is a profinite invariant (Book II, Part X).

Instances For

Tau.BookVI.Identity.instReprSelfDescOverCode

source instance Tau.BookVI.Identity.instReprSelfDescOverCode :Repr SelfDescOverCode

Equations

  • Tau.BookVI.Identity.instReprSelfDescOverCode = { reprPrec := Tau.BookVI.Identity.instReprSelfDescOverCode.repr }

Tau.BookVI.Identity.instReprSelfDescOverCode.repr

source def Tau.BookVI.Identity.instReprSelfDescOverCode.repr :SelfDescOverCode → ℕ → Std.Format

Equations

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

Tau.BookVI.Identity.selfdesc_code

source def Tau.BookVI.Identity.selfdesc_code :SelfDescOverCode

Equations

  • Tau.BookVI.Identity.selfdesc_code = { } Instances For

Tau.BookVI.Identity.SubstrateReplacement

source structure Tau.BookVI.Identity.SubstrateReplacement :Type

[VI.L08] Substrate Replacement Preserves Life-Equivalence. Complete material turnover (every atom replaced) does not alter life status, because SelfDesc evaluates code continuity, not material identity. Passes the metamorphosis test: caterpillar → chrysalis → butterfly preserves identity.

  • material_turnover : Bool Material turnover occurs.

  • code_preserved : Bool ω-germ code is preserved.

  • selfdesc_continuous : Bool SelfDesc evaluation is continuous through turnover.

  • metamorphosis_test : Bool Passes metamorphosis test (caterpillar → butterfly).

Instances For

Tau.BookVI.Identity.instReprSubstrateReplacement

source instance Tau.BookVI.Identity.instReprSubstrateReplacement :Repr SubstrateReplacement

Equations

  • Tau.BookVI.Identity.instReprSubstrateReplacement = { reprPrec := Tau.BookVI.Identity.instReprSubstrateReplacement.repr }

Tau.BookVI.Identity.instReprSubstrateReplacement.repr

source def Tau.BookVI.Identity.instReprSubstrateReplacement.repr :SubstrateReplacement → ℕ → Std.Format

Equations

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

Tau.BookVI.Identity.substrate_repl

source def Tau.BookVI.Identity.substrate_repl :SubstrateReplacement

Equations

  • Tau.BookVI.Identity.substrate_repl = { } Instances For

Tau.BookVI.Identity.identity_is_code_not_carrier

source theorem Tau.BookVI.Identity.identity_is_code_not_carrier :selfdesc_code.not_carrier = true ∧ selfdesc_code.profinite_invariant = true

Tau.BookVI.Identity.substrate_replacement_preserves_life

source theorem Tau.BookVI.Identity.substrate_replacement_preserves_life :substrate_repl.material_turnover = true ∧ substrate_repl.code_preserved = true ∧ substrate_repl.selfdesc_continuous = true ∧ substrate_repl.metamorphosis_test = true

Tau.BookVI.Identity.SubstrateAbstraction

source structure Tau.BookVI.Identity.SubstrateAbstraction :Type

[VI.T50] Substrate Abstraction Theorem. The 5 Distinction conditions (VI.D04) + 3 SelfDesc conditions (VI.D08) are necessary and sufficient for life, independent of material substrate. Proof: (1) Sufficiency: the definitions use only abstract morphisms, functors, and winding numbers — no material predicates appear. (2) Necessity: failure of any condition produces a counterexample (VI.D16 Absence catalog). (3) Independence: VI.L08 shows that replacing the material substrate while preserving code + evaluation preserves life-equivalence; VI.D53 locates identity in the code. Scope: τ-effective.

  • conditions_abstract : Bool All 8 conditions (5+3) are formulated abstractly.

  • sufficient : Bool 8 conditions are sufficient for life.

  • necessary : Bool 8 conditions are necessary for life (Absence catalog).

  • substrate_independent : Bool No material predicate appears in any condition.

  • scope : String Scope: τ-effective.

Instances For

Tau.BookVI.Identity.instReprSubstrateAbstraction.repr

source def Tau.BookVI.Identity.instReprSubstrateAbstraction.repr :SubstrateAbstraction → ℕ → Std.Format

Equations

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

Tau.BookVI.Identity.instReprSubstrateAbstraction

source instance Tau.BookVI.Identity.instReprSubstrateAbstraction :Repr SubstrateAbstraction

Equations

  • Tau.BookVI.Identity.instReprSubstrateAbstraction = { reprPrec := Tau.BookVI.Identity.instReprSubstrateAbstraction.repr }

Tau.BookVI.Identity.substrate_abs

source def Tau.BookVI.Identity.substrate_abs :SubstrateAbstraction

Equations

  • Tau.BookVI.Identity.substrate_abs = { } Instances For

Tau.BookVI.Identity.substrate_abstraction

source theorem Tau.BookVI.Identity.substrate_abstraction :substrate_abs.conditions_abstract = true ∧ substrate_abs.sufficient = true ∧ substrate_abs.necessary = true ∧ substrate_abs.substrate_independent = true