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Three O(1) reductions found in the existing codebase: 1. CRT gradient update (O(N²)→O(1) per crossing) Source: docs/research/unified_crt_torus_dag.md Energy update = one add, no recompute. Additivity of CRT residues. 2. CRT lift closed form (O(search)→O(1) formula) Source: archive/.../SidonWrapping.lean x = r₁ + L₁·((r₂−r₁)·L₁⁻¹ mod L₂). No search, one formula. 3. Adleman DNA computing (O(2ⁿ)→O(1) wet-lab steps) Source: archive/.../FOUNDATIONAL_GUIDANCE.md Lipton 1995: 2ⁿ assignments in parallel, O(1) lab operations. All three share: O(n) search → O(1) formula/physics → answer. Can they combine into a single O(1) transform? - They can be CHAINED (search→reconstruct→verify pipeline) - They cannot be MERGED (bottleneck is O(n) info extraction) - Conservation law: answer has O(n) bits, must read O(n) bits - Pipelining gives O(1) AMORTIZED per candidate (throughput, not latency) - True O(1) end-to-end requires all three in ONE physical step (DNA that hybridizes INTO a CRT-reconstructing structure that self-verifies) — speculative, not proven |
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| .. | ||
| braid_group_action.md | ||
| CAPABILITY_GRID_MAPPING.md | ||
| COLLECTIVE_INTELLIGENCE_OPTIMIZATION.md | ||
| COMPRESSION_HONEST_FINDINGS.md | ||
| FIXEDPOINT_BRIDGE_DESIGN.md | ||
| iteration_dag.md | ||
| iteration_regime.md | ||
| O1_TRANSFORMS.md | ||
| OCTAGON_PRINCIPLE.md | ||
| sidon_preservation_creation.md | ||
| unified_crt_torus_dag.md | ||