Topological Semantic Compression — Revised Framework

This record presents Topological Semantic Compression (TSC) together with an ML-native translation for alignment and interpretability research. In its revised form, TSC is not framed as compression in a strict information-theoretic sense, nor as a claim about proven formal topological invariants. Rather, it proposes a hypothesis-driven framework for narrative topology extraction and domain-appropriate reconstruction: the possibility that technical and mythic materials may sometimes reduce into compact cues because they share the same underlying ordered relational structure — patterns of roles, transitions, tensions, constraints, and resolutions that persist across domains. The framework argues that language models may not preserve exact semantic content across such reductions. Instead, they may recover and reconstruct relational story-shapes using whatever vocabulary is most available or appropriate to the target domain. On this account, the striking feature of the reported pilot results is not “lossless compression,” but the apparent preservation of narrative topology across cross-domain reconstruction. TSC therefore concerns preservation of relational structure under transformation, rather than extension of Shannon-style compression theory. The record includes the revised three-layer model, an illustrative compact cue example, framework-internal pilot metrics, and a blind reconstruction study across five language models. These materials are presented as exploratory and falsifiable, not as proof of a general law. The reported findings are offered as preliminary evidence consistent with the narrative topology hypothesis, while leaving open alternative explanations such as surface-level association priming or shared training-distribution effects. External validation and independent replication remain necessary next steps. This work forms part of the Recursive Equilibrium mathematical framework, which unifies RBE, HBE, MAF, and TSC into a single candidate stability architecture for AI systems. This version includes the revised source documents, archival PDF versions, and the pilot appendix materials associated with the TSC case study. Experimental Case Study (Appendix A)This record includes an illustrative pilot case study in which a technical sensor-fusion architecture and mythic narrative texts were jointly reduced into a single compact cue (approximately 197:1 reduction) and then reconstructed independently across five language model architectures. The notable result was not identical surface reconstruction, but domain-diverse reconstruction with structurally similar relational organisation. This outcome is consistent with the hypothesis that models may be responding to shared narrative topology rather than domain-specific semantics alone. The appendix is presented as a pilot observation documenting suggestive behavior, not as theoretical proof, benchmark evidence, or a claim of universal generalisability.