Legitimacy (recognition coherence)

Legitimacy, in the τ-framework, is the institutional reflex of justice: a τ-categorical condition where authority's commitment-stances form a coherent section on the recognition sheaf, survive the universalizability test, and preserve dignity for every recognized party. Legitimacy is the simultaneous satisfaction of three structural conditions — sheaf gluing on recognition, CI-stability, and dignity-preservation.

Categorical invariant. Λ = Sheaf-condition(recognition presheaf) ∧ Fix(CI-functor) ∧ Equalizer(dignity-action) on Reg_C; equivalently, an authority is legitimate iff its commitment-stance is a global section of the recognition sheaf that is also CI-closed and label-independent.

Primary registry anchor: VII.P25

Supporting items: VII.L40, VII.L41, VII.L42, VII.D77, VII.D04

1. I.K0 — Universe Postulate
2. VII.D04 — Commitment Register Reg_C with codomain Stance
3. VII.D77 — Sphere as Shared Topos — the institutional carrier of recognition
4. VII.L40 — Legitimacy Sheaf Connection — legitimacy = sheaf gluing on recognition sections
5. VII.L41 — Legitimacy Dignity Connection — legitimacy factors through dignity reflector
6. VII.L42 — Legitimacy from CI — legitimacy justification is CI universalizability
7. VII.P25 — Legitimacy as Recognition Coherence — canonical proposition

Legitimacy is instantiated whenever an institution's authority is recognized as binding because its commitment-stances cohere across constituents, survive universalizability, and preserve dignity. Examples: democratic mandate via free elections; constitutional review (judicial legitimacy via CI-test); central-bank credibility (technocratic legitimacy via track-record gluing); de-recognition of regimes that fail dignity preservation.

Examples:

• Democratic mandate — periodic election as recognition-sheaf gluing across the electorate
• Constitutional review — courts test legislation against CI-stability and dignity-preservation
• Central-bank independence and credibility — technocratic legitimacy via track-record sheaf
• International recognition of states — sheaf-gluing of inter-state recognition sections
• De-recognition of regimes (apartheid, juntas) — failure of dignity reflector triggers legitimacy collapse
• Indigenous sovereignty claims — recognition presheaf failing to glue under colonial overrides

Register codomain: Stance (Reg_C — legitimacy is the institutional global section of the recognition sheaf, factoring through both CI-fixed-point and dignity-equalizer)

Manuscript reference: manuscript-sources/book-07/part08/ch104.tex

Status: Skeleton

Module: TauLib.BookVII.Social.Ontology

Lean kind: structure

Lean symbol: Tau.BookVII.Social.Ontology.LegitimacyConditions

Related glossary entries

• MG-C01-dignity Dignity (label-independence)
• MG-C02-fairness Fairness (CI-protocol)
• MG-C03-justice Justice (gluing of fair stances)

Referenced by

• MG-C09-rights Rights (dignity-protected unearned section)
• MG-C11-trust Trust (admissibility expectation)