Practical Register (Reg_P)
The Practical Register Reg_P is the τ-categorical readout functor whose codomain is Norm (normative constraints): the structural interface between the τ-framework and action-guiding content. Reg_P is the second of four canonical readout functors (E/P/D/C). Its coherence criterion is normative consistency — the absence of contradictory obligations within a single action context.
τ-Definition
The Practical Register Reg_P is the τ-categorical readout functor whose codomain is Norm (normative constraints): the structural interface between the τ-framework and action-guiding content. Reg_P is the second of four canonical readout functors (E/P/D/C). Its coherence criterion is normative consistency — the absence of contradictory obligations within a single action context.
Categorical invariant. Functor Reg_P : K_τ → Norm whose image-objects are normative constraints (imperatives, obligations, permissions, prohibitions) and whose morphisms preserve normative consistency.
Primary registry anchor:
VII.D02
τ-Derivation Chain
Phenomenological Correlate
Reg_P is instantiated whenever a categorical claim is rendered as an action-guiding norm. Reg_P-content answers the question 'What should I do?' and delivers imperatives, obligations, permissions, and prohibitions. Examples: a maxim tested against the Categorical Imperative; a clinical protocol that obliges informed consent; a policy that forbids data exfiltration.
Examples:
- Categorical Imperative gluing — a maxim is universalisable iff it satisfies the sheaf condition on the dignity-filtered site (Reg_P-readout of VII.T31)
- Clinical informed-consent protocol — Reg_P-readout that delivers an obligation binding on the practitioner
- Institutional anti-corruption norm — Reg_P-readout of a sector-S_P content into a contradiction-free obligation set
Register codomain: Norm (normative constraints; obligations, permissions, prohibitions; coherence = normative consistency)
Manuscript reference: manuscript-sources/book-07/part01/ch03.tex
Lean Coverage
Status: Planned