Step 006 — Counting as construction

For each generator g, the expression ${\phi }_g\left(n\right)={\rho }^n\left(g\right)$ is not a classification of pre-existing numbers.

Book / layer. Book I · E0
Macro step. CS-01 — Build the τ-Kernel
Short routes. https://prrp.site/s6 · https://prrp.site/s006

Status tags. formal

Construction role

For each generator g, the expression ${\phi }_g\left(n\right)={\rho }^n\left(g\right)$ is not a classification of pre-existing numbers. It is the generated count itself: the n-th finite application of ρ along an orbit. Counting therefore appears first as constructive depth, not as imported ℕ, and it must be kept separate from later calculation inside earned algebraic structures. The metalanguage may index this process by n, but the τ-object is the generated orbit position.

What this step earns

Counting as construction is made addressable as Step 006 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:196)

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 005 — Nonredundant fold strata
• Next: Step 007 — Iterator ladder

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