Trust (admissibility expectation)

Trust, in the τ-framework, is the expectation of Commitment Register Admissibility: a τ-categorical relation in which one agent assigns prior probability one (or near-one) to another agent's future Reg_C-updates satisfying the four admissibility conditions of VII.D72. Trust is the social precondition that lets the Reg_C-network function as a sheaf — when trust collapses, the recognition presheaf fails to glue and legitimacy collapses with it.

Categorical invariant. Τ = the relation Tr(σ, τ) on agent pairs such that σ assigns probability ≈ 1 to U_promise(τ, ·) being admissible in future contexts; equivalently, σ accepts τ's Reg_C-readouts as gluing-compatible without requiring local re-verification. Trust is the subjective precursor of legitimacy on the recognition sheaf.

Primary registry anchor: VII.D72

Supporting items: VII.D04, VII.D67, VII.P25, VII.D70

1. I.K0 — Universe Postulate
2. VII.D04 — Commitment Register Reg_C with codomain Stance
3. VII.D70 — Character as Ethical Fixed Point — the long-run substrate that warrants trust
4. VII.D67 — Fairness Protocol — trust is rational only when the trusted party's stances are CI-closed
5. VII.D72 — Commitment Register Admissibility — trust is the expectation of admissibility
6. VII.P25 — Legitimacy as Recognition Coherence — institutional trust at sphere-level

Trust is instantiated whenever an agent accepts another's Reg_C-readouts as gluing-compatible without local re-verification. Examples: interpersonal trust (close relationships, repeat games); institutional trust (banks, courts, science); credentialing systems (peer review, professional licensure); the breakdown of trust as canonical signal of legitimacy collapse.

Examples:

• Interpersonal trust in close relationships — high-prior admissibility expectation built from observed character (VII.D70)
• Institutional trust in banks and courts — sphere-level trust, the substrate of monetary and legal Reg_C
• Trust in science — admissibility expectation on peer-review-validated readouts of Reg_E gluing with Reg_C
• Professional licensure (medicine, law, engineering) — credential as institutional trust witness for VII.D72
• Trust collapse as legitimacy signal — bank runs, science replication crises, post-truth politics
• Algorithmic trust (zero-trust networks, cryptographic protocols) — engineered admissibility under adversarial assumption
• Reconciliation processes — explicit re-construction of a damaged trust relation as precondition for re-gluing the recognition sheaf

Register codomain: Stance (Reg_C — trust is the meta-stance assigning admissibility-prior to another agent's future Reg_C-updates; the subjective precursor of the recognition sheaf's gluing condition)

Manuscript reference: manuscript-sources/book-07/part07/ch90.tex

Status: Planned

Related glossary entries

• MG-C05-character Character (ethical fixed point)
• MG-C06-legitimacy Legitimacy (recognition coherence)
• MG-C07-promise Promise / Commitment (admissible Reg_C-update)