Step 023 — Earned constants π_τ,e_τ,j

The first structural constants are read from already-earned geometry and iteration.

Book / layer. Book II · E0
Macro step. CS-02 — Recover Core Mathematics
Short routes. https://prrp.site/s23 · https://prrp.site/s023
Formula checkpoints. ${\pi }_{\tau }$ · $e_{\tau }$ · j · $2_{\tau }$

Status tags. formal hinge

Construction role

The first structural constants are read from already-earned geometry and iteration. ${\pi }_{\tau }$ is obtained from the internal Euclidean/incidence geometry; $e_{\tau }$ from the eigenvalue structure of the -iterator; j from the split-complex idempotent boundary algebra. The dyadic scalar

is the two-channel/refinement scalar read from the earned idempotent boundary split, not the imported natural number 2. None of these constants is imported from ordinary real or complex analysis. Each records a different internal stabilization: geometric closure, iterative growth, and bipolar boundary decomposition.

What this step earns

Earned constants ${\pi }_{\tau }$, $e_{\tau }$, j is made addressable as Step 023 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:348)

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 022 — Tarski geometry and wave-type causal precursor
• Next: Step 024 — Master constant ι_τ

Navigate

• 100-Step Routing Ledger
• Ten-step Construction Spine