Step 018 — τ³ as geometric readout τ¹×_f T²

The geometric object denoted ${\tau }^3$ is constructed as a readout of τ, not adopted as a Cartesian product.

Book / layer. Book II · E0
Macro step. CS-02 — Recover Core Mathematics
Short routes. https://prrp.site/s18 · https://prrp.site/s018
Formula checkpoints. ${\tau }^3$ · ${\tau }^3$

Status tags. formal hinge

Construction role

The geometric object denoted ${\tau }^3$ is constructed as a readout of τ, not adopted as a Cartesian product. It is not τ×τ×τ. The base ${\tau }^1$ is the (D,A) radial/address base of the ABCD chart; the fiber $T^2$ is the (B,C) solenoidal fiber built from the two bipolar character channels. The fiber map f records the nontrivial dependency, so no global trivialization

is asserted. This fibered readout is the canonical geometric body that later becomes the substrate candidate for the Book-III physical carrier.

What this step earns

as geometric readout ${\tau }^1$×_f $T^2$ is made addressable as Step 018 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:294)

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 017 — Boundary-first inversion
• Next: Step 019 — Cylinders and ultrametric topology

Navigate

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