Step 030 — Kernel minimality and categoricity
The construction uses three distinct notions of uniqueness, and the document keeps them separate.
The construction uses three distinct notions of uniqueness, and the document keeps them separate.
Book / layer. Book II · E0
Macro step. CS-03 — Internalize Self-Enrichment
Short routes. https://prrp.site/s30 · https://prrp.site/s030
Status tags. formal
Construction role
The construction uses three distinct notions of uniqueness, and the document keeps them separate. First, at E0, the operative claim is minimal constructive sufficiency: the five generator symbols, ρ, and K0 – K6 are claimed to be the least symbolic source able to carry address structure, topology, holomorphy, self-enrichment, and the E1 carrier. Fewer generators should collapse the construction; additional generators should be redundant or break canonical closure. Second, at the Central-Theorem level, the rank-(3,15) categoricity check says that the relevant fibered product with an ABCD chart satisfying K0 – K5 is canonically isomorphic to ; at that rank the moduli space is pt. Third, classical model-theoretic categoricity – one model up to isomorphism over arbitrary models – belongs to the later E3 self-hosting problem, where τ can represent formal systems, model talk, and its own kernel internally. This dossier uses the first two notions and defers the third.
What this step earns
Kernel minimality and categoricity is made addressable as Step 030 in the fine-grained Construction Spine routing layer.
- Routing scaffold. Detailed earned-output extraction is pending the source-map pass.
What this step does not yet establish
This route exposes the RC3 construction step for inspection. It does not by itself establish peer review, empirical adequacy, or final manuscript-level source closure.
Source anchors
- Full Construction Spine RC3 whitepaper source (papers/whitepapers/panta-rhei-construction-spine-e0-e3/main.tex:439)
Manuscript extraction state: Detailed source anchors pending extraction.
Anchor classification: whitepaper source resolved; manuscript extraction pending; Registry extraction pending; TauLib extraction pending.
Formalization and verification
Registry links: Registry extraction pending.
TauLib modules: TauLib module extraction pending.
Dependencies
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