In January 2026 two papers were deposited on Zenodo establishing that information loss at dimensional boundaries in discrete systems is a geometric phenomenon with an architecture-independent magnitude: 86.01% ± 2.39% in cellular automata across 1,500 patterns (Thornhill 2026b, DOI 10.5281/zenodo.18262424, 01/14/2026), and 84.39% ± 1.55% on transformer hidden states (GPT-2, Gemma-2), supported by a formal proof of the component transformations S, R, and D (Thornhill 2026c, DOI 10.5281/zenodo.18319430, 01/20/2026). It was predicted, in the closing discussion of Thornhill 2026c, that the geometric account should hold across substrates wherever density dilution and neighborhood-structure expansion occur together at a representational boundary. In March 2026, Barman, Starenky, Bodnar, Narasimhan, and Gopinath independently published two arXiv preprints (arXiv:2603.27116 and arXiv:2604.06222) reporting that production retrieval embedding models — MiniLM-L6-v2, BGE-base, BGE-large — concentrate their variance into approximately 16 effective dimensions regardless of nominal dimensionality (384, 768, 1024), and that this concentration places those models in an interference-vulnerable geometric regime that reproduces quantitative signatures of human memory failure (power-law forgetting with exponent b = 0.460 ± 0.183, Deese–Roediger–McDermott false-alarm rate of 0.583, spacing-effect ordering, tip-of-tongue behavior). They establish a parallel theorem — the No-Escape Theorem — characterizing what cannot be repaired within semantically continuous kernel-threshold memory systems. The two bodies of work are methodologically distinct. They use different metrics (Φ = R·S + D vs. participation ratio), study different substrates (cellular automata and transformer hidden states vs. pretrained retrieval embeddings), and report different specific quantities (an 86% loss constant in Φ vs. a fixed point at ~16 effective dimensions across nominal sizes). They also reach the same broader conclusion from independent directions: that representational memory failure is a geometric property of the embedding operation, not a property of any particular architecture, training regime, or biological substrate. The present note records the chronology of the two lines of evidence in a single citable document, summarizes the methodological differences, and identifies the substantive convergence: an architecture-independent geometric fixed point as the principal explanatory mechanism for representational memory failure in the systems studied.

This is a synthesis note bridging two parallel lines of evidence on the geometric structure of representational memory failure. The author's prior work (Thornhill 2026b, DOI 10.5281/zenodo.18262424, deposited 01/14/2026; Thornhill 2026c, DOI 10.5281/zenodo.18319430, deposited 01/20/2026) established the dimensional-loss constant in cellular automata and transformer hidden states. Barman et al. (arXiv:2603.27116, arXiv:2604.06222, posted 03/28/2026 and 03/27/2026 respectively) report parallel findings on production retrieval embedding spaces using participation-ratio methodology. The present note positions both contributions on a single citable surface and identifies the substantive convergence at the level of architecture-independent geometric fixed points without claiming numerical equivalence between the specific quantities reported by the two methodologies.