Step 005 — Nonredundant fold strata
The four non-ω rays are not arbitrary names, and their indices are not introduced as pre-given primes.
The four non-ω rays are not arbitrary names, and their indices are not introduced as pre-given primes.
Book / layer. Book I · E0
Macro step. CS-01 — Build the τ-Kernel
Short routes. https://prrp.site/s5 · https://prrp.site/s005
Status tags. hinge
Construction role
The four non-ω rays are not arbitrary names, and their indices are not introduced as pre-given primes. Their canonical roles are fixed at the fold level: α supplies direct counting, π the future multiplicity spine, γ the future exponent channel, η the future tetration channel, and ω the fixed-point absorber and closure beacon. The fold-chain principle then orders the operations: progression-depth supplies counting; addition is recovered over progression-depth; multiplication, exponentiation, and tetration are successive finite folds; and the ladder saturates at the η-level, with no fourth finite fold admitted as a canonical new address layer. Primality is still unavailable here: only after multiplication and divisibility are earned does the internal prime enumeration identify the scalar prime-readout sequence 2,3,5, rather than import it. Prime-addressability is therefore earned by fold structure, while ω remains the global iteration boundary: ρ(ω)=ω and ρ^n(g)≠ω for non-ω generators.
What this step earns
Nonredundant fold strata is made addressable as Step 005 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:194)
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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