Diagrammatic Sector (S_D)

The Diagrammatic Sector S_D is the collection of all E_3-admissible contents whose coherence is governed by the Diagrammatic Register Reg_D. Formally, S_D = { c ∈ Adm_{E_3} | Coh(c) = Coh_D(c) }. Its sector question is 'What can I prove?', its witness bundle is a structural proof, and its vacuum is a maximally certified body of structural results. S_D contains the Logos sector S_L as the locus where Coh_D = Coh_C.

Categorical invariant. Subobject S_D ⊆ Adm_{E_3} cut out by the equation Coh = Coh_D. Third of four pure sectors; weakly contains S_L via the equality Coh_D|_{S_L} = Coh_C|_{S_L}.

Primary registry anchor: VII.D09

Supporting items: VII.D03, VII.D11, VII.D07, VII.D08, VII.D10

1. I.K0 — Universe Postulate
2. VII.D03 — Diagrammatic Register Reg_D with codomain Proof
3. VII.D09 — Diagrammatic sector S_D — admissible contents whose coherence equals diagrammatic coherence
4. VII.D11 — Logos sector S_L ⊆ S_D — the mixed-sector intersection where Coh_D = Coh_C

S_D is instantiated wherever a category-error-free claim's coherence is governed by proof-validity: a Lean-checked theorem, a categorical universal property, a worked derivation. The sector question — 'What can I prove?' — is the structural ground of categorical aesthetics, language and meaning, and logic and inference (Book VII, Parts IV–VI).

Examples:

• A Lean-formalised theorem with finite witness chain — sector S_D content whose vacuum is maximal certification
• The Yoneda Lemma as theorem in H(τ) — sector S_D content read out by Reg_D (Book II, Part 8)
• A worked derivation in the CI proof programme (dignity → CI as j-closed fixed point) — sector S_D content that earns the Reg_P-readable norm

Register codomain: Proof (via Reg_D); the sector itself is a subobject of Adm_{E_3}

Manuscript reference: manuscript-sources/book-07/part01/ch05.tex

Status: Planned

Related glossary entries

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