Corpus Construction Step Scaffolded Address geometry is made global by hyperfactorization.
Construction StepScaffolded

Step 009 — Hyperfactorization and ABCD chart

Address geometry is made global by hyperfactorization.

Address geometry is made global by hyperfactorization.

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/s9 · https://prrp.site/s009

Status tags. formal hinge

Construction role

Address geometry is made global by hyperfactorization. Every X≥ 2 receives a unique decomposition X=((A↑↑ C)^B)· D as a tower atom T(A,B,C)=(A↑↑ C)^B multiplied by a residual D. At this point divisibility and internal primality have already been earned. In the τ-statement, A is the largest internal prime atom (under idx, the largest prime divisor of X), C is the maximal tetration height of the A-tower factor, B is the residual tower exponent, and D has only internal prime factors strictly less than A. The resulting ABCD chart, written in later scalar notation as

:ℕ_≥ 2 to P×ℕ_≥ 1^3,

is injective and turns arithmetic objects into typed global addresses. This prevents number from collapsing into a flat additive/multiplicative background and preserves the tower structure needed for boundary polarity downstream.

What this step earns

Hyperfactorization and ABCD chart is made addressable as Step 009 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:202)

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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