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
