The Incorruptible Rule of Law: Synthesizing the Non-Lying Kernel (NLK), René Thom's Butterfly Catastrophe (A_5), Contradictory Provenance Roots, and the Gatekeeper Omega Open Cylinder Against the Coercive Axis of the Welfare State // Den Ubestikkelige Rettsstaten: Syntesen av Den Ikke-Løgnende Kjerne (NLK), René Thoms Sommerfugl-Katastrofe (A_5), Kontradiktorisk Proveniensrot og Portvokteren Omega mot Velferdsstatens Tvangsakse (Document 197 // SPEC-400, v2.0)

Document 197 (SPEC-400, v2.0, Bilingual Norwegian & English Edition) — Four-Pillar Synthesis of Document 160 (Gatekeeper Omega: Persistence Without Recurrence, DOI: 10.5281/zenodo.22924845), Document 162 (NLK v2.0, DOI: 10.5281/zenodo.23448706), Document 195 (The Coercive Axis of the Welfare State, DOI: 10.5281/zenodo.23647132), and Document 196 (René Frédéric Thom and the Catastrophe of Form, DOI: 10.5281/zenodo.23645980):

Four Interlocked Pillars:

1. From Cusp Coercion (A₃) to the Butterfly Safe Harbor (A₅, 2.50 V HOLD): Demonstrates how the 0.4 G disability income allowance, 75–80 % effective marginal clawback/tax rate, and reassessment risk in the National Insurance Act operate as an unstable Cusp catastrophe (V''(0) = a < 0) forcing economic lock-in, and how lifting the allowance (≥ 1.25 G) with 100 % statutory protection of the disability rating creates a structurally stable Butterfly safe harbor (V''(0) = c > 0).
2. Bilateral Contradictory Provenance Root (W_t^bilat) & Ma'at's Involution F(F(s)) = s: Replaces the unilateral administrative/clinical case record monopoly (Health Personnel Act §§ 39–43) with an append-only SHA-256 Merkle chain binding the institution's assessment and the citizen's unabridged adversarial protocol with equal weight. Recoding legal dissent as a symptom triggers GATE::KILL (0.00 V DC).
3. Semiophysics (Saillance vs. Prégnance) & Cobordism Protection (∂² = 0): Enforces GENERATION != AUTHORIZATION != REALIZATION != PROOF against speculative clinical prognoses and circular FARV capacity-to-consent invalidation, requiring unconditional suspensive effect prior to any depot neuroleptic intervention.
4. Gatekeeper Ω (Document 160): Persistence Without Recurrence on the Open Cylinder X = S¹ × R × WORM: Resolves the bureaucratic closed-circle fallacy by proving that when a citizen's cyclic health/work phase θ(t) ∈ S¹ returns to a rest state after a work attempt (relapse), the state space never closes (dL(W_t^bilat)/dt > 0); any administrative attempt to erase or zero out accumulated entitlement history upon relapse triggers GATE::KILL (0.00 V DC), while Carnot equilibrium (ΔS_total = 0.0000 J/K) and irrational foliation {π, e, √2} preserve individual trajectory integrity.

Epistemic Demarcation (AGENTS.md): INSPIRED_BY != IMPLEMENTS != PROVES · L1_LOCAL_SOFTWARE_PROTOTYPE (8/8 unit tests passing) · AKUERISAAVOQ.