Step 065 — Lorentzian signature from j²=+1

The Lorentzian / Minkowski signature is read from the split-complex hyperbolicity already earned in Book I – II.

Book / layer. Book V · E1
Macro step. CS-06 — Build Measurement, Prediction, and Empirical Bridges
Short routes. https://prrp.site/s65 · https://prrp.site/s065
Formula checkpoints. $j^2$

Status tags. readout external-validation-seam

Construction role

The Lorentzian / Minkowski signature is read from the split-complex hyperbolicity already earned in Book I – II. Because $j^2$, the carrier grammar carries null directions and causal cones before an external Lorentzian metric is imposed. Light cones are therefore the causal cones of the split-complex carrier readout. The remaining bridge question is physical: whether this algebraic cone structure reproduces the full empirical Lorentzian regime.

What this step earns

Lorentzian signature from $j^2$ is made addressable as Step 065 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:896)

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 064 — τ-Einstein identity
• Next: Step 066 — Thermodynamic inversion

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