Justice (gluing of fair stances)
Justice, in the τ-framework, is the sheaf-gluing of fair commitment-stances across the social base: a τ-categorical condition where local fairness verdicts (Reg_C readouts of individual cases) agree on overlaps and assemble into a globally coherent section. Justice is the categorical pasting of fairness, not a higher principle imposed on top of it.
τ-Definition
Justice, in the τ-framework, is the sheaf-gluing of fair commitment-stances across the social base: a τ-categorical condition where local fairness verdicts (Reg_C readouts of individual cases) agree on overlaps and assemble into a globally coherent section. Justice is the categorical pasting of fairness, not a higher principle imposed on top of it.
Categorical invariant. Justice = the global section of the fairness presheaf Φ on the recognition site; equivalently, J = lim Φ over the cover of relevantly-similar cases. A society is just iff its fair-stance presheaf glues to a sheaf.
Primary registry anchor:
VII.D43
τ-Derivation Chain
-
I.K0— Universe Postulate -
VII.D04— Commitment Register Reg_C with codomain Stance -
VII.D67— Fairness Protocol — local CI-procedure -
VII.D74— Earned/Unearned Ethics Framework — basis for distributive cases -
VII.D43— Justification as Gluing — local-data agreement on overlaps -
VII.P25— Legitimacy as Recognition Coherence — institutional reflex of justice
Phenomenological Correlate
Justice is instantiated whenever local fairness verdicts on similar cases must cohere on their overlaps. Examples: equal-protection doctrine (like cases treated alike); precedent-based common law (gluing of past rulings); restorative-justice circles (community-level coherence between victim, offender, and community sections).
Examples:
- Equal protection under law — like cases treated alike (sheaf condition on legal Reg_C readouts)
- Stare decisis / precedent — common-law gluing of past rulings into a coherent juridical sheaf
- Distributive justice (Rawls' difference principle) — globally coherent fairness across socioeconomic strata
- Restorative-justice circles — community-level gluing of victim, offender, and bystander stances
- Transitional justice (truth and reconciliation) — re-gluing a fractured social sheaf
Register codomain: Stance (Reg_C — justice is the global section of the fairness presheaf on the recognition site)
Manuscript reference: manuscript-sources/book-07/part03/ch34.tex
Lean Coverage
Status: Planned