PRF0004activev1Conditional Proof of Categoricity of τ_0
Conditional proof of Categoricity of τ_0 (THM0009). Completes the categoricity argument under the named bridge axiom (AXM0001 bridge-functor- exists). Without that bridge, the proof reduces to a sketch.
Payload
Proof
Conditional proof. This proof depends on explicit unresolved assumptions and should not be read as complete until those assumptions are discharged.
The categoricity argument is complete *conditional* on the bridge functor F: τ-Cat → Orth-Cat existing (AXM0001). Without that axiom discharged, the proof is a sketch; with it, categoricity follows.
Proof steps
- Universal property setup.
Establish the universal property of τ_0 from the τ-Kernel construction (see THM0001 for the master constant anchoring the calibration).
Uses:
prrp://thm0001@v1(uses theorem) - Bridge functor invocation (conditional).
Under the bridge-functor-exists axiom AXM0001, the universal property reflects through F into the orthodox category, fixing the τ_0 representation uniquely.
Uses:
prrp://axm0001@v1(uses assumption) - Categoricity follows.
From s1 + s2 + the rigidity of τ (THM0008), categoricity of τ_0 is established up to canonical isomorphism.
Uses:
prrp://thm0008@v1(uses theorem)
Identifiers
Aliases & legacy IDs
proof-categoricity-conditionalRelease lines
corpus_v3_workingRelations
Upstream dependencies (3)
Version & History
Status disclaimer
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