Corpus Construction Step Scaffolded Once progression depth exists, addition is recovered as the finite fold of ρ on the τ-index scaffold.
Construction StepScaffolded

Step 007 — Iterator ladder

Once progression depth exists, addition is recovered as the finite fold of ρ on the τ-index scaffold.

Once progression depth exists, addition is recovered as the finite fold of ρ on the τ-index scaffold.

100-step ledger status. This page is scaffolded from the Full Construction Spine RC3 whitepaper. Whitepaper source anchors are present; deeper manuscript, Registry, and TauLib anchors are intentionally marked pending until the source-map extraction pass promotes them.
Macro context. CS-01 — Build the τ-Kernel

Book / layer. Book I · E0
Macro step. CS-01 — Build the τ-Kernel
Short routes. https://prrp.site/s7 · https://prrp.site/s007

Status tags. formal

Construction role

Once progression depth exists, addition is recovered as the finite fold of ρ on the τ-index scaffold. The higher ladder then folds successively: multiplication is iterated addition, exponentiation is iterated multiplication, and tetration is iterated exponentiation. Thus raw ρ underlies the four concrete address levels +, ×, exponentiation, and tetration, which saturate at tetration. Algebra enters as disciplined recursion over generated symbolic depth. The inspection question is whether this ladder truly derives the operations from ρ, or whether ordinary arithmetic re-enters through the external recursion language.

What this step earns

Iterator ladder is made addressable as Step 007 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:198)

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

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