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  "text": "@fnruji316625 @frankniujc Shapes are projected not discovered.\n\nΩ: the space of all possible outputs\nE: the prompt expanse — outputs reachable from query q as prior over the training distributions, the input keyhole \nS: the stencil — the projection selected from E(q)\n\nS(q) ⊂ E(q) ⊂ Ω\n\nThe vector prior is already a keyhole. Inference narrows it further. What appears as a “shape” is a stencil projected over the reachable expanse E(q), not a direct view into the manifold itself.\n\nIf q traverses a dense region of E(q), the projection appears coherent and filled in. If not, the structure collapses into noise or omission. This tells us about the relationship between q and E(q), not about any internal persistent geometric objects.\n\nNo shape survives arbitrary changes in prior, temperature, or sampling path. What persists is not the projection, but the constraints that generate it.\n\nInterpretability must first explain those constraints before treating projected shapes as intrinsic structure.",
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