IndisputableMonolith.Governance.InstitutionalFailureFromJCost
This module establishes that each governance institution maps to exactly one failure mode derived from J-cost in the Recognition Science framework. Researchers modeling institutional collapse or regulatory design would cite the bijection when analyzing systemic risks. The module consists of type definitions for institutions and modes plus a bijection lemma that enforces uniqueness.
claimEach institution $I$ has a unique failure mode $F$ via the map $Imapsto F$ with the bijection ensuring one-to-one correspondence between the set of institutions and the set of failure modes.
background
The module imports the RS time quantum $τ_0=1$ tick from IndisputableMonolith.Constants. It introduces GovernanceInstitution as the type of formal institutions, FailureMode as the discrete set of collapse patterns, and institutionFailureMode as the function assigning the unique mode to each institution. The local theoretical setting is the governance domain where J-cost accumulation determines institutional stability.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the unique-failure-mode axiom that higher governance theorems would invoke when deriving collapse thresholds from J-cost. It fills the step linking recognition costs to institutional outcomes in the Recognition Science chain.
scope and limits
- Does not quantify J-cost thresholds for failure onset.
- Does not address multi-institution interactions or cascades.
- Does not derive failure modes from explicit phi-ladder rungs.