Step 020 — Stone/profinite shape and two-readout principle

The ultrametric cylinder topology is compact, Hausdorff, and totally disconnected: a Stone/profinite shape.

Book / layer. Book II · E0
Macro step. CS-02 — Recover Core Mathematics
Short routes. https://prrp.site/s20 · https://prrp.site/s020

Status tags. formal

Construction role

The ultrametric cylinder topology is compact, Hausdorff, and totally disconnected: a Stone/profinite shape. This does not contradict the later geometric readout, because τ carries two compatible readouts of the same earned structure. The profinite readout preserves refinement, limit, and address information; the geometric readout gives the body on which incidence, fiber structure, and later carrier projection can be read. The fine Stone/profinite topology and coarse geometric readout are parallel consequences of the same address/coherence data. The two-readout principle prevents either side from being collapsed into the other: geometry is not topology, but it is canonically read from the same address structure.

What this step earns

Stone/profinite shape and two-readout principle is made addressable as Step 020 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:317)

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

• Previous: Step 019 — Cylinders and ultrametric topology
• Next: Step 021 — Geometric lemniscate at ω

Navigate

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