Step 021 — Geometric lemniscate at ω

The algebraic lemniscate of Book I now receives a geometric body.

Book / layer. Book II · E0
Macro step. CS-02 — Recover Core Mathematics
Short routes. https://prrp.site/s21 · https://prrp.site/s021

Status tags. hinge

Construction role

The algebraic lemniscate of Book I now receives a geometric body. At the ω-boundary, the $T^2$-fiber degenerates into a wedge locus whose two lobes correspond to the B-polar and C-polar character channels. Boundary, wedge, and character-ring residence coincide at this locus. The point is not decorative: the same bipolar grammar that organized split-complex boundary characters now appears as the limiting geometry of the fiber.

What this step earns

Geometric lemniscate at ω is made addressable as Step 021 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:330)

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 020 — Stone/profinite shape and two-readout principle
• Next: Step 022 — Tarski geometry and wave-type causal precursor

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