TauLib · API Book I

TauLib.BookI.MetaLogic.OnticInvariance

TauLib.MetaLogic.OnticInvariance

Ontic Identity Invariance theorem, No Identity Decoherence corollary, and the Slippage Breaks Unique Omega theorem.

Registry Cross-References

  • [I.T46] Ontic Identity Invariance — ontic_identity_invariance

  • [I.C03] No Identity Decoherence — no_identity_decoherence

  • [I.T47] Slippage Breaks Unique Omega — slippage_breaks_omega

Mathematical Content

The Ontic Identity Invariance theorem shows that τ’s coherence kernel preserves ontic identity at every construction step. The corollary establishes that diagonal resonance cannot occur. The conditional theorem shows identity slippage prevents unique omega internalization.

Tau.MetaLogic.BlockingMechanism

source inductive Tau.MetaLogic.BlockingMechanism :Type

[I.T46] The three mechanisms that block diagonal resonance in τ.

  • k5_diagonal_discipline : BlockingMechanism
  • nf_confluence : BlockingMechanism
  • star_autonomous_structure : BlockingMechanism Instances For

Tau.MetaLogic.instDecidableEqBlockingMechanism

source instance Tau.MetaLogic.instDecidableEqBlockingMechanism :DecidableEq BlockingMechanism

Equations

  • Tau.MetaLogic.instDecidableEqBlockingMechanism x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

Tau.MetaLogic.instReprBlockingMechanism

source instance Tau.MetaLogic.instReprBlockingMechanism :Repr BlockingMechanism

Equations

  • Tau.MetaLogic.instReprBlockingMechanism = { reprPrec := Tau.MetaLogic.instReprBlockingMechanism.repr }

Tau.MetaLogic.instReprBlockingMechanism.repr

source def Tau.MetaLogic.instReprBlockingMechanism.repr :BlockingMechanism → ℕ → Std.Format

Equations

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

Tau.MetaLogic.blocking_targets

source def Tau.MetaLogic.blocking_targets :BlockingMechanism → ResonanceComponent

Each blocking mechanism targets a specific resonance component. Equations

  • Tau.MetaLogic.blocking_targets Tau.MetaLogic.BlockingMechanism.k5_diagonal_discipline = Tau.MetaLogic.ResonanceComponent.L
  • Tau.MetaLogic.blocking_targets Tau.MetaLogic.BlockingMechanism.nf_confluence = Tau.MetaLogic.ResonanceComponent.E
  • Tau.MetaLogic.blocking_targets Tau.MetaLogic.BlockingMechanism.star_autonomous_structure = Tau.MetaLogic.ResonanceComponent.P Instances For

Tau.MetaLogic.blocking_targets_injective

source **theorem Tau.MetaLogic.blocking_targets_injective (m1 m2 : BlockingMechanism)

(h : blocking_targets m1 = blocking_targets m2) :m1 = m2**

The blocking map is injective: each mechanism targets a distinct component.

Tau.MetaLogic.blocking_targets_surjective

source theorem Tau.MetaLogic.blocking_targets_surjective (c : ResonanceComponent) :∃ (m : BlockingMechanism), blocking_targets m = c

The blocking map is surjective: every component has a blocker.

Tau.MetaLogic.allBlockingMechanisms

source def Tau.MetaLogic.allBlockingMechanisms :List BlockingMechanism

All blocking mechanisms enumerated. Equations

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

Tau.MetaLogic.blocking_mechanism_count

source theorem Tau.MetaLogic.blocking_mechanism_count :allBlockingMechanisms.length = 3

There are exactly 3 blocking mechanisms.

Tau.MetaLogic.OnticIdentityInvariance

source structure Tau.MetaLogic.OnticIdentityInvariance :Type

[I.T46] Ontic Identity Invariance: in the coherence kernel, every admissible construction preserves ontic identity. Formalized as: τ has a blocker for each resonance component, and its resonance profile is clean.

The proof packages together:

  • K5 blocks (L) — contraction_present = false

  • NF-confluence blocks (E) — equality_congruence = false

  • Star-autonomous blocks (P) — self_products = false

  • profile : DiagonalResonance τ’s resonance profile

  • is_tau : self.profile = tau_resonance The profile matches τ

  • l_blocked : self.profile.contraction_present = false (L) is blocked

  • e_blocked : self.profile.equality_congruence = false (E) is blocked

  • p_blocked : self.profile.self_products = false (P) is blocked

  • all_blocked
    (c : ResonanceComponent)
    ∃ (m : BlockingMechanism), blocking_targets m = c All three blocking mechanisms exist

Instances For

Tau.MetaLogic.ontic_identity_invariance

source def Tau.MetaLogic.ontic_identity_invariance :OnticIdentityInvariance

The theorem witness: τ satisfies all conditions. Equations

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

Tau.MetaLogic.identityCoherenceLevel

source def Tau.MetaLogic.identityCoherenceLevel (dr : DiagonalResonance) :ℕ

Identity coherence level: 100% means no component of diagonal resonance is present. Equations

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

Tau.MetaLogic.tau_identity_coherence_100

source theorem Tau.MetaLogic.tau_identity_coherence_100 :identityCoherenceLevel tau_resonance = 100

τ has 100% identity coherence.

Tau.MetaLogic.orthodox_identity_coherence_0

source theorem Tau.MetaLogic.orthodox_identity_coherence_0 (f : OrthodoxFoundation) :identityCoherenceLevel (orthodox_resonance f) = 0

Orthodox foundations have 0% identity coherence (all three components present).

Tau.MetaLogic.no_identity_decoherence

source theorem Tau.MetaLogic.no_identity_decoherence :tau_resonance.isFullResonance = false

[I.C03] No Identity Decoherence: the diagonal resonance pattern (L+E+P) cannot occur at the ontic level in τ. Direct consequence of I.T46.

Tau.MetaLogic.no_partial_decoherence

source theorem Tau.MetaLogic.no_partial_decoherence :tau_resonance.contraction_present = false ∧ tau_resonance.equality_congruence = false ∧ tau_resonance.self_products = false

Stronger form: no subset of the resonance components is present.

Tau.MetaLogic.UniqueOmegaCapability

source structure Tau.MetaLogic.UniqueOmegaCapability :Type

A foundation can internalize unique omega only if it has no identity slippage.

  • resonance : DiagonalResonance
  • no_resonance : self.resonance.isFullResonance = false No full resonance (prerequisite for unique omega)

Instances For

Tau.MetaLogic.slippage_breaks_omega

source **theorem Tau.MetaLogic.slippage_breaks_omega (dr : DiagonalResonance)

(h : dr.isFullResonance = true) :¬∃ (u : UniqueOmegaCapability), u.resonance = dr**

[I.T47] Slippage Breaks Unique Omega: a foundation with full diagonal resonance cannot internalize a unique absolute infinity omega.

If identity slippage is present (full resonance = true), then UniqueOmegaCapability is impossible for that resonance profile.

Tau.MetaLogic.tau_omega_capability

source def Tau.MetaLogic.tau_omega_capability :UniqueOmegaCapability

τ CAN internalize unique omega (because it has no resonance). Equations

  • Tau.MetaLogic.tau_omega_capability = { resonance := Tau.MetaLogic.tau_resonance, no_resonance := Tau.MetaLogic.tau_no_full_resonance } Instances For

Tau.MetaLogic.orthodox_no_omega

source theorem Tau.MetaLogic.orthodox_no_omega (f : OrthodoxFoundation) :¬∃ (u : UniqueOmegaCapability), u.resonance = orthodox_resonance f

All orthodox foundations CANNOT internalize unique omega (full resonance).