Diagrammatic Register (Reg_D)

The Diagrammatic Register Reg_D is the τ-categorical readout functor whose codomain is Proof (structural proofs): the interface between the τ-framework and proof-bearing content. Reg_D is the third of four canonical readout functors (E/P/D/C). Its coherence criterion is proof-validity — every claim admits a finite witness chain terminating in kernel axioms.

Categorical invariant. Functor Reg_D : K_τ → Proof whose image-objects are structural proofs (witness chains, derivations, diagram-certified relationships) and whose morphisms preserve proof-validity.

Primary registry anchor: VII.D03

Supporting items: VII.D09, VII.D11, VII.D01, VII.D02, VII.D04

1. I.K0 — Universe Postulate
2. VII.D03 — Diagrammatic Register Reg_D with codomain Proof
3. VII.D09 — S_D (diagrammatic sector) — the τ-sector that Reg_D reads
4. VII.D11 — Logos sector S_L — the unique location where Reg_D and Reg_C coincide

Reg_D is instantiated whenever a categorical claim is rendered as a structural proof. Reg_D-content answers the question 'What can I prove?' and consists of structural demonstrations, mathematical theorems, logical deductions, and diagram-certified relationships. Examples: a Lean-checked theorem; a categorical limit certified by a universal-property diagram; a worked derivation of the central theorem in Book II.

Examples:

• Lean-formalised theorem with finite witness chain terminating in kernel axioms (Reg_D-readout of a τ-derivation)
• Yoneda Lemma as theorem in H(τ) — Reg_D-readout of a categorical universal property (Book II, Part 8)
• Categorical-imperative proof programme: dignity → CI as j-closed fixed point (the diagrammatic-side derivation that earns the practical-side norm)

Register codomain: Proof (structural proofs; finite witness chains terminating in kernel axioms; coherence = proof-validity)

Manuscript reference: manuscript-sources/book-07/part01/ch03.tex

Status: Planned

Related glossary entries

• MG-R01-empirical-register Empirical Register (Reg_E)

Referenced by

• MG-A04-temporalization-operators Temporalization Operators
• MG-A05-pragmatic-update-operator Pragmatic Update Operator
• MG-P02-or2-finite-signature OR2 Finite Signature
• MG-P08-layer-discipline Layer Discipline (Register Discipline)
• MG-P11-truth-bearer Truth-Bearer as Section