Corpus Construction Step Scaffolded Prime polarity cannot remain a bare classification of fold strata: it must be given an algebra in which the two polar orientations can be projected, compared, and later transported.
Construction StepScaffolded

Step 012 — Split-complex boundary algebra

Prime polarity cannot remain a bare classification of fold strata: it must be given an algebra in which the two polar orientations can be projected, compared, and later transported.

Prime polarity cannot remain a bare classification of fold strata: it must be given an algebra in which the two polar orientations can be projected, compared, and later transported.

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/s12 · https://prrp.site/s012

Status tags. hinge

Construction role

Prime polarity cannot remain a bare classification of fold strata: it must be given an algebra in which the two polar orientations can be projected, compared, and later transported. The construction therefore passes to the bipolar boundary algebra

𝔻τ=Rτ⊕jRτ

, j2=+1j² = +1 ,

where R_τ denotes the earned scalar/readout algebra available at this stage, not an imported real line. Its idempotents

e_±=(1± j)/(2)

split boundary behavior into orthogonal channels, and the σ-equivariant Boolean sublattice

B_σ(D)=0,e_+,e_-,1

gives the first four-atom boundary grammar. At this stage the atoms are not physical sectors; they are pre-physical channel eigenstates with the pre-physics dictionary 0 null, e_+γ/B, e_-η/C, 1α/D. Physical names such as electromagnetic, strong, and gravitational are assigned only after the Book-III carrier and sector readout are constructed.

What this step earns

Split-complex boundary algebra is made addressable as Step 012 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:212)

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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