Step 039 — 3+1 spacetime signature

The fibered shape already separates the base ${\tau }^1$ from the $T^2$-fiber.

Book / layer. Book III · E1
Macro step. CS-04 — Identify the Physical Carrier
Short routes. https://prrp.site/s39 · https://prrp.site/s039

Status tags. bridge

Construction role

The fibered shape already separates the base ${\tau }^1$ from the $T^2$-fiber. After global Cartesian gluing, the $T^2$-derived bulk supplies the spatial readout, while the ${\tau }^1$-base supplies the temporal direction that Book V will develop as proper time. The resulting 3+1 signature is therefore not chosen as a background Lorentzian metric. It is the structural signature of the carrier: three spatial directions from the Hartogs bulk, one temporal base direction from ${\tau }^1$.

What this step earns

3+1 spacetime signature is made addressable as Step 039 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:573)

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 038 — Global Cartesian gluing and decompactification
• Next: Step 040 — 4+1 sector template

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