Conjecture 1: Nonunital Anticoncentration Obstruction

Big Picture

Conjecture 1 asks whether realistic primitive nonunital noise keeps local random-circuit output distributions from strongly anticoncentrating even when the noise has finite temporal memory and spatial locality. The current goal is not to rebuild the Markovian theorem; it is to lift the known Markovian nonunital obstruction into a bounded-memory process-tensor setting.

Current Status

• The theorem anchor is markovian-nonunital-anticoncentration-obstruction.md.
• The non-Markovian language is organized by process-tensor-framework.md and instrument-specific-finite-quantum-markov-order.md.
• The comparison regime is unital-noisy-random-circuit-uniformization.md: unital noise can drive uniformity, while nonunital noise preserves a different obstruction.
• The current synthesis node is bounded-markov-order-nonunital-extension-candidate.md.

Next Actions

1. Fix the first bounded-memory model class: bounded Markov order process tensors, hidden-Markov amplitude damping, or collision models.
2. Try to lift only the second-moment inequality before attempting a Porter-Thomas total-variation separation.
3. Identify whether the conjecture's diamond-norm memory-decay hypothesis implies an effective finite-memory transfer operator with constants independent of circuit depth.

Local Files

• Research map
• Zotero actions report
• Learning stub
• Manuscript stub