Step 015 — Lemniscate characters

With the four-valued boundary algebra in place, boundary behavior can be organized into characters.

Book / layer. Book I · E0
Macro step. CS-01 — Build the τ-Kernel
Short routes. https://prrp.site/s15 · https://prrp.site/s015

Status tags. formal

Construction role

With the four-valued boundary algebra in place, boundary behavior can be organized into characters. The characters χ_± read the two idempotent channels of 𝔻 and assemble them into the algebraic lemniscate: the bipolar locus where B-polar and C-polar tower behavior meet without collapsing into one channel. This gives the boundary a character ring, not merely a set of truth values. Book II will later supply the geometric readout of this algebraic lemniscate: the $T^2$-fiber degenerates at ω into the wedge locus that carries the same character grammar.

What this step earns

Lemniscate characters is made addressable as Step 015 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:254)

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 014 — Four-valued τ-topos
• Next: Step 016 — Global Hartogs

Navigate

• 100-Step Routing Ledger
• Ten-step Construction Spine