3212 — Input, Output, and Control Form Three Coherence Towers
The programme is better typed as three towers over a shared labelled state: input constructibility, output observability, and control coherence. A state may be input-detectable, control-preserved, and output-null simultaneously.
The RH-bearing theorem must therefore be a natural cross-tower Ward cell: output zero-state boundary conditions, transported through a control Green identity, must annihilate every finite input-curvature packet. Input joint faithfulness can then exclude the nonzero off-seam state.
Durable verification
- Research packet: research/grothendieck/input-output-and-control-form-three-coherence-towers.md
- Exact checker: research/grothendieck/checkers/check_three_towers_need_cross_coherence.py
- Sequence claim: seqclaim-273ec636abed7543a5a2a8d1
- Graph event: ev-000000006706-f0de8a82-cd89-4a6f-b4d6-da0e51b189ac