Algorithm 1 LTA-Alignment with LLM Arbiter

Input: Candidate entity pair (ei,ej), Total linear length Ltotal, Semantic threshold [τlow,τhigh], Gaussian tolerance σ. Output: Alignment decision D∈{Merge,Reject} 1: Phase 1: Gaussian Topological Penalty Computation 2: Extract semantic embeddings vi,vj for ei,ej 3: Simsem ← CosineSimilarity(vi,vj) 4: Extract absolute physical distances li,lj for ei,ej 5: $\mathrm{Compute}\mathrm{normalized}\mathrm{manifold}\mathrm{anchors}:\mathsf{\Phi }\left(e_i\right)\leftarrow {\displaystyle \frac{l_i}{L_{total}}},\mathsf{\Phi }\left(e_j\right)\leftarrow {\displaystyle \frac{l_j}{L_{total}}}$ 6: $\mathrm{Compute}\mathrm{absolute}\mathrm{spatial}\mathrm{deviation}:\delta \leftarrow \left|\mathsf{\Phi }\left(e_i\right)-\mathsf{\Phi }\left(e_j\right)\right|$ 7: $\mathrm{Compute}\mathrm{topological}\mathrm{penalty}\mathrm{multiplier}:Si{m}_{top}\leftarrow exp\left(-{\displaystyle \frac{{\delta }^2}{2{\sigma }^2}}\right)$ 8: $\mathrm{Compute}\mathrm{composite}\mathrm{alignment}\mathrm{score}:S\leftarrow Si{m}_{sem}\times Si{m}_{top}$ 9: Phase 2: Grey-Zone Arbitration Logic 10: if S < τlow then 11:      $\mathcal{D}\leftarrow Reject$ (Short-circuit rejection) 12: else if S > τhigh then 13:      $\mathcal{D}\leftarrow Merge$ (Direct unconditional merge) 14: else (Grey-Zone triggered) 15:      Cctx ← ExtractContext(ei,ej) (e.g., timestamps, worker logs) 16:      Pprompt ← ConstructPrompt(ei,ej,Cctx) 17:      decision_result ← LLM_Arbiter(Pprompt) 18:      if decision_result == “Yes” then 19:          $\mathcal{D}\leftarrow Mege$ 20:      else 21:          $\mathcal{D}\leftarrow Reject$ 22:          end if 23: end if 24: return: $\mathcal{D}$