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Cross-referenced against our prover orchestration layers: - Plan-Execute-Verify-Replan ↔ L0-L3 pipeline - Agents as specialists ↔ 11-agent swarm - Guardrails ↔ ProverWatchdog - Sandbox testing ↔ Virtual FPGA tests - Trajectory-aware eval ↔ BFS audit trail 5 gaps identified, 4 strengths confirmed
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985 B
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9 lines
985 B
Text
created: 20260507000000000
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modified: 20260507000000000
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tags: ResearchStack Lean PIST Compression Math
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title: PIST Shell Encoding
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type: text/vnd.tiddlywiki
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! PIST Shell Encoding
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PIST (Prime Integer Shell Transform) encodes integers as (k, t) coordinates where n = k² + t, k = floor(sqrt(n)), 0 ≤ t ≤ 2k. Formalized in `0-Core-Formalism/lean/Semantics/Semantics/PIST.lean` with bridges to hardware blitter via `PistBridge.lean`. Mass is t·(2k+1-t) — zero at shell edges, max at center. Mirror involution (k, t) → (k, 2k+1-t) preserves mass and is self-inverse. Extensions: n-dimensional bundle shifting (`PistNDBundleShifter`), phi-shell golden ratio encoding (`PhiShellEncoding.lean`), torsional PIST variants. The Python implementations span 5 files at `3-Mathematical-Models/pist_biological_polymorphic_shifter_v3*.py` and `5-Applications/pist-scripts/`. Visualizable via `3-Mathematical-Models/cad_models/pist_shells.scad`. One of three pathological manifold structures.
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