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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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9 lines
917 B
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created: 20260507000000000
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modified: 20260507000000000
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tags: ResearchStack Lean Q16_16 FixedPoint
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title: Fixed Point Algebra
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type: text/vnd.tiddlywiki
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! Fixed Point Algebra
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Q16_16 fixed-point arithmetic formalized in `0-Core-Formalism/lean/Semantics/Semantics/FixedPoint.lean` — provides 16-bit integer + 16-bit fractional representation with formal proofs of algebraic properties. All physics computations in the stack use Q16_16 (per AGENTS.md §1.4). Includes arithmetic operations (add, sub, mul, div), comparison operators, conversion to/from floats, and formal theorems proving non-overflow bounds, associativity, and distributivity. The `FixedPointBridge.lean` connects Q16_16 to hardware extraction targets. Q32_32 variant under development with formal verification tools (`4-Infrastructure/shim/use_provers_to_fix_q32_32.py`). Related to the [[Lean Semantics Overview]] and hardware extraction pipeline.
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