Counterfactual Neuro-Symbolic Proof-Carrying Memory for Auditable Multi-Hop Reasoning on Unstructured Data

Knowledge-intensive language understanding suffers a structural reliability bottleneck: fluent answers can be produced without logically sufficient support, especially in multi-hop question answering and dynamic knowledge graphs where edge drift degrades retrieval. We introduce Counterfactual Neuro-Symbolic Proof-Carrying Memory (CNS-PCM), a backbone-agnostic neuro-symbolic harness that decouples frozen neural representations from inspectable symbolic verification checks. Candidate reasoning chains are discovered via ontology-constrained beam search ($\Gamma$) and compiled into a compact proof-carrying memory carrying crisp domain validity flags (${\kappa }_k$), NLI-derived contradiction scores (${\rho }_k$), and textual support confidences (${\alpha }_k$). At inference time, a counterfactual verifier stress-tests prediction stability across a targeted pool of $J=12$ graph interventions sampled via betweenness centrality, requiring $\mathcal{O}(J·K·d)$ localized re-scoring operations over the $K\le 16$ retained proofs (or $\mathcal{O}(J·d)$ at fixed memory capacity K, where empirical proof depth satisfies $d\le 3$ for $>94\%$ of retained paths under a search ceiling $m_{\max }=6$, bounding verifier latency overhead to ≈45 ms per query), and abstains when evidence is unstable. Rather than invasive early token fusion or prompt linearization, CNS-PCM externalizes verification into an inspectable audit record while training lightweight adapter heads using task, logical-consistency, intervention-invariance, and differentiable Brier calibration objectives. Evaluated on official public splits of HoVer, HotpotQA, and FEVEROUS with headline F1 scoring ABSTAIN as incorrect, CNS-PCM achieves test F1 scores of $80.6\%$, $75.2\%$, and $79.0\%$, outperforming LLaMA-2-7B + CoT ($72.4\%/67.1\%/70.2\%$), GraphRAG ($78.5\%/73.8\%/77.4\%$), and unthresholded Logic-LM ($79.1\%/74.1\%/77.9\%$). Specifically, CNS-PCM reduces total gold-unsupported accepted assertions on the validation splits by up to $2.4$ percentage points (lowering total unsupported rate from $16.4\%$ to $14.7\%$, and correct-but-ungrounded assertions from $6.8\%$ to $5.3\%$) and reduces Expected Calibration Error (ECE) to $6.5\%$, maintaining $95.2\%$ final test coverage via a bounded re-try feedback loop ($\overline{R}=0.471$ re-tries). Component ablations confirm that training invariance and inference gating provide complementary gains, while sensitivity analyses identify Stage-2 entity linking as the primary reliability lever.