Same Problem, Different Slices: The Geometry of Ideological Non-Exit

This paper addresses a persistent paradox: why structurally similar problems generate irreconcilable interpretations and sustain long-term conflict.

We argue that such divergence cannot be fully explained by differences in values, information, or reasoning alone. Instead, we propose that interpretations arise from distinct “slices” of a shared underlying structure (Φ_total), and that conflict emerges as a consequence of geometric divergence across these slices.

Extending the slice model, we introduce a structural framework consisting of:
- slice formation (projection of underlying structure),
- position in state-space (MMS),
- directional drift (FARL),
- and transition feasibility governed by Slice Transition Cost (STC).

We show that persistent conflict is best understood not as disagreement, but as a loss of transition capacity. As STC increases, alternative interpretive states remain formally present but become structurally inaccessible, leading to non-exit conditions.

Within this framework, sustainable systems are not those that eliminate disagreement, but those that preserve:
- slice multiplicity,
- low transition cost,
- and recoverability.

This work provides a geometric account of ideological conflict, reframing polarization as a structural problem of transition rather than a failure of consensus.

This work is an exploratory contribution situated within the IPCSALT–UPF phase-based meta-framework.