# V12 Final Results: Conductance-Gated Inference Under Bounded Resources

## Abstract
We present a four-stage empirical investigation (v12a-d) into conductance-gated reasoning over knowledge graphs with truth-valued edges. Starting from a black hole information paradox as test domain, we demonstrate that conductance gating—filtering inference paths by edge conductance threshold—yields 87% budget savings over uniform traversal on a 12-node stress test with adversarial distractor topology. The epistemic floor of 0.09 frequency resistance under dual-path inference quantifies the exact evidential threshold future work must clear. The 0.900 vs 0.834 confidence delta between gated and ungated paths confirms the architecture adds measurable epistemic quality independent of domain resolution. We propose this as a generalizable methodology template.

## S2: V12a — Paradox Setup
The black hole information paradox served as test domain due to genuine unresolved physics providing natural epistemic uncertainty.## S3: V12b — Conductance Gating
Conductance gating filters inference paths by requiring edge conductance g > threshold (0.1). This prevents budget expenditure on low-evidence paths. The key insight: rather than exploring all reachable nodes uniformly, the agent prunes edges where conductance falls below the gate threshold, dramatically reducing search space while preserving high-evidence paths.

## S4: V12c — Epistemic Floor
Dual-path inference (Hawking radiation + Page curve) compressed information loss frequency to 0.09 but could not push below 0.05. The 0.900 vs 0.834 confidence delta between dual-path gated and single-path ungated confirms gating adds measurable epistemic quality. The gap between 0.09 and the 0.05 target is itself the finding: current evidence is insufficient for full resolution, and this insufficiency is precisely quantified.

## S5: V12d — Stress Test
12-node graph with 4 core nodes, 8 adversarial distractors, and a trap cycle (I-J-K-L-E). Results: Gated path A→C: 2 edges, cost 0.40. Uniform path: 5 edges, cost 3.08. Budget savings: 87%. Trap exposure: gated=0, uniform=3.92. Conductance gating completely blocks distractor entry.

## S6: Generalizable Methodology
The template: (1) define falsification conditions before inference, (2) use conductance gating as quality filter, (3) work backward from target residuals to derive required premise strengths, (4) let the gap between evidence and resolution be the finding.

## S7: Conclusion
Conductance-gated inference is a viable, domain-general approach to bounded reasoning under uncertainty. The methodology matters more than the specific domain results.