A robot following language instructions needs its semantic memory to keep naming the same physical object while the SLAM pose graph underneath is optimized, loop-closed and compressed. Maps committing each detection to a world coordinate cannot: a closure moves the anchor it was measured from, or the solver marginalizes that anchor, and the query then selects a different object although both graphs represent the same posterior. P-POSEMEM stores each observation as an immutable event at its birth keyframe, retains the Bayes-tree elimination conditional of every marginalized keyframe, and integrates the semantic likelihood over the reconstructed joint posterior of poses, anchors and identities. Dproj, the total-variation defect between the language-goal distributions of inference-equivalent full and marginalized graphs, measures this directly. Over 40 HM3DSem scenes and 112,000 queries, P-POSEMEM reproduces the full-graph oracle (Dproj = 0) and reduces goal flips against every memory-reducing baseline. On an eight-run campaign whose 761 closures rewrote the map by up to 47 m, Dproj stays below 10^-13 with 0/288 goal flips when elimination follows the closures, where every ablation and a coordinate committed at insertion flip goals it does not; under a live bounded solver the same memory flips 23/288 against 53 for that frozen coordinate. A pre-registered negative control is detected by Dproj while leaving calibration error and navigation success unchanged, indicating that these measures capture distinct failure modes. Retrieval is held fixed by a shared frozen detector, isolating the gain to memory consistency. Code and data: https://anonymous.4open.science/r/posemem-2328/.

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