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Orthogonal tensor (hypercube) assumes independent axes. Shear into parallelotope (hyper-rhomboid) models entangled dimensions. The shear angle encodes correlation strength; the Gram matrix of the shear IS the compression dictionary. 6 stack mappings: - PIST n-D: Cartesian → Bundle → Radial = hypercube → rhomboid → collapsed - Topological state machine: transition = shear on state tensor - N-D Gene Hypothesis: gene = n-D rhomboid, 3D structure = projection shadow - FAMM: preshaped delay = sheared time-domain rhomboid - OAC: latent cavity in sheared rhomboid space - Waveprobe: curvature = local shear angle of coordinate basis 3 compression interpretations + information gravity metric tensor
15 lines
1.2 KiB
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15 lines
1.2 KiB
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created: 20260507000000000
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modified: 20260507000000000
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tags: ResearchStack TSM Topology Manifold
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title: Topological State Machine
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type: text/vnd.tiddlywiki
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! Topological State Machine
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The Topological State Machine (TSM) is a geometric state-evolution framework that models manifold transitions as discrete steps through topological space. Core implementation: `5-Applications/scripts/topological_state_machine.py`. Extended variants: eigenvector TSM (`eigenvector_tsm_hyperfluid.py`), Hutter TSM (`hutter_eigenvector/`), and unified hypersurface TSM (`3-Mathematical-Models/unified_surface/`). State data stored in `3-Mathematical-Models/topological_state_machine/` with `tsm_report_*.json` outputs. Uses [[FAMM Fast Approximate Manifold Map]] for caching state transitions. Integration with Lean via `TopologicalStateMachine.lean`. The TSM cache directories (eigenvector_tsm, hutter_eigenvector) contain FAMM banks for fast manifold lookup. Referenced in the [[ENe Cognitive Refactor Plan]] Phase 6 for shell-partitioned cache eviction.
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* [[FAMM Fast Approximate Manifold Map]]
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* [[Lean Semantics Overview]]
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* [[Manifold Flow]]
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* [[Semantic Eigenvector Bundle]]
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* [[Unified Hypersurface]]
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