Step 026 — Regularity and finite spectral support

The admissible maps of Step 25 must also be regular in a finite, inspectable sense.

Book / layer. Book II · E0
Macro step. CS-02 — Recover Core Mathematics
Short routes. https://prrp.site/s26 · https://prrp.site/s026

Status tags. formal

Construction role

The admissible maps of Step 25 must also be regular in a finite, inspectable sense. Within the τ-holomorphic category, regularity is the positive finite-stabilization condition: at p, the ω-germ/evolution sequence stabilizes at some finite primorial depth N. Equivalently, the B- and C-channel regularity conditions both stabilize, so the canonical idempotent-supported extension exists. Regularity is therefore not imposed as an external analytic smoothness condition; it is finite stabilization of the earned boundary/evolution grammar.

What this step earns

Regularity and finite spectral support is made addressable as Step 026 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:384)

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 025 — Local Hartogs and mutual determination
• Next: Step 027 — Sheaf coherence, self-enrichment, Yoneda

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