Corpus Construction Step Scaffolded After internal primes and CRT idempotents are available, prime polarity is fixed by the CRT-local/spectral-Legendre classifier, not by the ABCD growth-rate comparison alone.
Construction StepScaffolded

Step 010 — Prime polarity

After internal primes and CRT idempotents are available, prime polarity is fixed by the CRT-local/spectral-Legendre classifier, not by the ABCD growth-rate comparison alone.

After internal primes and CRT idempotents are available, prime polarity is fixed by the CRT-local/spectral-Legendre classifier, not by the ABCD growth-rate comparison alone.

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/s10 · https://prrp.site/s010

Status tags. hinge

Construction role

After internal primes and CRT idempotents are available, prime polarity is fixed by the CRT-local/spectral-Legendre classifier, not by the ABCD growth-rate comparison alone. For odd p, p is B-labelled iff (2/p)=+1 iff p≡±1±od 8, and C-labelled iff (2/p)=-1 iff p≡±3±od 8; 2 carries the mixed X-label. The τ-derivation lives at the idempotent level in H_τ Z/Primorial(n) Z, via CRT idempotents and spectral Legendre reduction, and agrees pointwise with the orthodox Legendre classifier. Both B and C classes are infinite, indeed density 1/2. The older growth-rate story is structural motivation, not the derivation.

What this step earns

Prime polarity is made addressable as Step 010 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:208)

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

Save or share this page for inspection

Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.

Email to expert